As Robusto suspected (see the comments), the protagonist, Lieutenant Eve Dallas, is indeed a police officer. She is the heroine in the …in Death series of novels by the author J. D. Robb (real name Nora Roberts). In the series, Lieutenant Dallas's eyes are several times described as cop-flat, meaning, unexpressive and unreadable eyes of a police officer.
The meaning of cop-flat
That cop-flat means, roughly, 'unexpressive and unreadable eyes of a police officer' is especially clear here, in a passage from another novel in the series:
Her narrow, angular face was set, the long golden brown eyes cop flat. Unreadable even to him.
(from Divided in Death)
So to say that Eve's eyes are cop-flat is to say that eyes of cops are often characteristically flat, and that Eve's eyes were just like that. Here the relevant dictionary meaning of flat is 'lacking in animation, zest, or vigor : dull' (Merriam-Webster); 'lacking interest or emotion; dull and lifeless' (Oxford Dictionaries); 'Wanting in points of attraction and interest; prosaic, dull, uninteresting, lifeless, monotonous, insipid.' (Sometimes with allusion to flat drink, i.e. one that has lost its flavour or sharpness; dead, insipid, stale.) 'Said of composition, discourse, a joke, etc. Also of a person with reference to his composition, conversation, etc.' (OED).
Parsing the sentence quoted by the OP
The passage quoted by the OP is from Obsession in Death. The sentence
Now she stood a moment, a tall, slim woman with short, tousled brown hair, with long-lidded eyes of gilded brown cop-flat in her angular face.
is relatively difficult to parse and it may even seem at first glance that cop-flat is used as a noun—indeed, it might seem that gilded brown cop-flat is a nominal (a noun phrase without a determiner), where the adjective phrase gilded brown modifies the noun cop-flat. But that is not so. Here is the same sentence, where I've restored some words that were ellipted in the original:
…a tall, slim woman… with long-lidded eyes of gilded brown color that were cop-flat in her angular face.
Here is an analogous construction, where wet from the rain plays the role of cop-flat in her angular face:
This is a woman with shoes of beautiful purple [color that were] wet from the rain.
Here color that were can be ellipted without changing the meaning of the sentence, though it will be harder to parse.
Other examples of usage of cop-flat
Here are some other instances from the series where Eve's eyes are described as cop-flat:
Bystanders gathered just outside the sidewalk barricades. She scanned them with eyes the color of good Irish whiskey, and cop flat. And spotted the witness in the back of a blackand-white.
(from Mirror, Mirror)
She paused, her eyes going cop flat.
(from Loyalty in Death)
In addition, at least one other author has used cop-flat, too:
Those eyes would be her best feature, except they were cop flat.
(from Reluctant Burglar by Jill Elizabeth Nelson)
Finally, a related construction appears in yet another book:
Billard tilted his head to the side and regarded Coop with his cop's flat eyes.
(from The Night Caller by John Lutz)
The grammar of cop-flat
Based on various parts of CGEL, it seems that cop-flat is best considered an adjective-centred compound adjective. If that is right, then it should always be hyphenated (contrary to how it appears in many of the books mentioned above). In particular, cop-flat should not be considered a syntactic construction, i.e. it shouldn't be considered an adjective phrase (AdjP) in which a noun modifes an adjective. According to CGEL, 'adjectives take only a highly restricted type of NP [noun phrase] as pre-head dependent' (p. 1656). On pp. 549–550, CGEL lists the allowable types of NP pre-head dependents: they are either measure phrases (as in three years old, five centimetres thick, a foot wide, two hours long, …), or else quantificational NPs (as in a bit lax, a smidgin overripe, a tad greasy, a trifle shy, plenty big enough, …). Some quantificational ones occur only with comparatives (a great deal smaller, a (whole) lot different, lots better, heaps worse, …). But in all cases, notice they are truly complete noun phrases (NPs), meaning that they include a determiner when one is necessary. In contrast, we have cop-flat, not *a cop flat. This is an indication that we are not dealing with a syntactic construction (an adjective phrase), but rather with a compound one.
Here is the relevant discussion from CGEL (p. 1656).
4.3.1 Adjective-centred compound adjectives
■ Noun + adjective compounds
The majority of compounds with an adjective as second component have a noun as the first. In general, there is no contrast here between a compound and a syntactic construction since adjectives take only a highly restricted type of NP as pre-head dependent (cf. Ch. 6, §3.2): the syntactic dependents of adjectives are generally pre-head adverbs or post-head PPs and clauses. Many noun + adjective compounds involve a high degree of lexicalisation, as in:
 colour-fast foot-loose headstrong threadbare top-heavy
Although there is a more or less obvious connection between the meaning of the whole and that of the adjective head, none of these satisfy the test for hyponymy. He is headstrong, for example, does not entail He is strong, and something can be top heavy even though it is as a whole relatively light. We will not attempt a comprehensive review of the patterns to be found, but will illustrate a selection of the more productive ones.
 i bone-dry crystal-clear dirt-cheap dog-tired feather-light
ice-cold paper-thin razor-sharp rock-hard stone-deaf
ii bottle-green brick-red jet-black snow-white steel-blue
Here the noun indicates a standard of comparison: "dry as a bone", "clear as crystal", etc. Very often, as in [i], the effect is to intensify: bone-dry means "extremely/completely dry", and so on. A special case of the comparative type is that of colour adjectives, as in [ii]; jet-black and snow-white are intensifying, but the others simply specify a particular shade of the colour. Compounds of this type are clearly hyponymic: if you are dog-tired, then necessarily you are tired, and so on.
 ankle-deep shoulder-high skin-deep state-wide week-long
This is a productive pattern, with the noun indicating extent. Wide here has to do with area rather than the one-dimensional measure denoted by wide on its own, and skin-deep "superficial" is a further example of lexicalisation. Compounds formed on this pattern are non-hyponymic: The water was ankle-deep, for example, does not entail The water was deep. We noted earlier that there may be a variety of reasons why a compound might fail the hyponymy test: in the present case it is due to the fact that the adjectives are gradable ones that can apply either to the scale generally (How deep is the water?) or to an area of the scale greater than some relevant norm (The water is deep). The compound involves the first use, whereas the adjectives are generally interpreted in the second way when standing alone.
 accident-prone burglar-proof camera-shy carsick cholesterol-free
class-conscious girl-crazy oil-rich power-mad praiseworthy
snow-blind tax-free travel-weary user-friendly watertight
These are comparable to syntactic constructions where the adjective has a following PP as dependent, complement, or modifier - compare prone to accidents, proof against burglars, crazy about girls, rich in oil, etc. Free (both in the sense "not having to pay", as in tax-free, and in the sense "not containing", as in cholesterol-free) is particularly productive. Some adjectives, such as crazy, free, mad, rich, weary, worthy, occur readily both in compounds and in syntactic constructions, while others, such as proof and tight, prefer or require the compound form.26 Others again take syntactic complements but hardly form compounds: fond of animals, keen on sport, eager for revenge (compare *animal-fond, *sport-keen/*sports-keen, *revenge-eager). Where the noun corresponds to a syntactic complement, the compounds are generally not hyponymic: tax-free goods aren't (necessarily) free, nor is a user-friendly computer manual a friendly one. With prone and proof the issue does not in fact arise since they cannot stand alone without complements - and indeed the same applies to free and conscious in the senses they have in cholesterol-free and class-conscious.
26Fail-safe and tamper-proof are exceptional in that the first base is a verb rather than noun.
There is another type that involves compounds with self (self-confident, self-conscious, self-evident, self-important, self-righteous), but that's clearly not relevant.
We've said that cop-flat is an adjective-centred compound adjective; now the question becomes, of what type? It is not comparative/intensifying: the noun cop does indicates a standard of comparison—the author is not trying to say that her eyes were as flat as that of a cop, but rather that they had the quality of flatness that is characteristic of cops. Cop-flat is also not a measure term, for the same reason. Moreover, measure terms are not supposed to be hyponymic, but cop-flat is: her eyes being cop-flat does imply they were flat. The final category, that of incorporated complement/modifier, seems to fit the best. First of all, some examples of it are hyponymic: being travel-weary does imply that one is weary, for example. Also, cop-flat is indeed comparable to a syntactic construction where the adjective has a following PP as dependent, complement, or modifier: to say that Eve's eyes were cop-flat is to say that Eve's eyes were flat in the manner of a cop's eyes.