My spellcheck doesn't complain about 'uniquer'. Is it a valid word?
Since unique means "one of a kind", 'uniquer' has no valid definition, but that doesn't prevent it from being a valid dictionary word.
Spellcheckers are never to be absolutely trusted. When in doubt, the dictionary should always come in handy. Indeed, we colloquially modify "unique" all the time, as in quite unique, very unique, and really unique! This usage is rightly frowned upon by an overwhelming majority, considering the meaning of the word "unique":
being the only one of its kind; unlike anything else
particularly remarkable, special, or unusual
( unique to) belonging or connected to (one particular person, group, or place)
New Oxford American Dictionary, 2nd Edition
The question of whether or not unique can be compared is a matter of debate among experts of the English language. Here's a note on usage from Merriam-Webster:
Many commentators have objected to the comparison or modification (as by somewhat or very) of unique, often asserting that a thing is either unique or it is not. Objections are based chiefly on the assumption that unique has but a single absolute sense, an assumption contradicted by information readily available in a dictionary... In modern use both comparison and modification are widespread and standard but are confined to the extended senses...
The "extended senses" would be the bulleted ones in my Oxford definition. And here is one more quote from Wiktionary:
Unique in its undisputed sense is not comparable. In its disputed senses, however, it can be compared as more unique, most unique, and occasionally as uniquer, uniquest.
Thus, uniquer can be considered valid within a proper context.
The comparative form of "unique" is "more unique", not "uniquer".
"More unique" has gotten some opprobrium, in large part because of its association with the hyperbole of marketing, but the complaint one sometimes sees that the term is "illogical" is unjustified.
Talking about whether something is "unique" always comes with an implicit reference: something is unique if it is "the only one of its kind," but this only moves us on to the question of when two things have the same kind. To get at the ambiguous edges of the word, consider a handcrafted, custom-made table, with a design and shape unlike that of any other. Now consider a hundred tables, all handcrafted by the same person, each one with a different shape and design from the others. Now consider a hundred thousand tables, each one with a different shape and design, generated by a computer algorithm designed to ensure that no two are exactly the same. In this last case, at least, there's a strong argument that while each of these hundred thousand tables is different in design from any other, they are no longer particularly unique.
So talking about whether something is "more unique" is an assertion that it is unique relative to a weaker notion of when two things have the same kind---that is, it is still unique even when more things are "the same kind" and therefore fewer things are unique.
I'd try not to use "uniquer". It's better if you use "more unique".
That is uniquer than a dinosaur bone.
That is more unique than a dinosaur bone.
I'd try and use the second example, but the first one may also be "correct".
NOTE: Of course, you could always say "uniquer" until someone points out that your grammar needs some revising. Then you could most kindly point out to them that you've encountered the word before in that form, and it was correctly used.
I think the best that can be said for it is that it can be valid grammatically while still being logically ridiculous. There is nothing in the language that prohibits one from that construction other than intelligence and good judgment.