TL;DR: There is no possible ordering of these two suffixes at all.
They are in complementary distribution and cannot be ordered in any way.
What are -ness and -less
What you fail to realise is that the two suffixes are not added as a group to a single word (despite what dictionaries may tell you): they are both addable, individually, to various types of words.
-ness forms abstract nouns from adjectives (occasionally also from nouns or noun phrases—like wilderness, which is historically from *wild deer-ness—though this is not productive1).
-less forms adjectives from nouns and sometimes verbs (tireless, for example—also not really productive).
As you can see, this makes for rather a reciprocal definition: -ness takes adjectives and makes them nouns; -less takes nouns and makes them adjectives.
In other words:
If you take a base noun (say, spot) and add -less, you create a new word: a derived adjective, spotless. Add -ness to that, and you create another new word: a derived noun, spotlessness.
If you take a base adjective (say, kind) and add -ness, you create a derived noun, kindness. Add -less to that, and you create a derived adjective, kindnessless.
In both these cases, you could theoretically continue the cycle ad nauseam, or at least until you no longer have the faintest idea what what you’re saying is supposed to mean (is something that is spotlessnesslessnesslessnessless clean or dirty? Heaven knows!). This process is part of what is known as recursion: applying a process to an input that is itself the result of the process you’re applying.
Continuing the cycle more than once or twice is highly impractical, obviously, but it does plays perfectly by the rules of English morphology, and the main reason it’s not practically usable is that English speakers cannot keep that level of abstraction and repeated negation in their heads. That’s a semantic constraint, a limitation in the part of our brains that attach logical meaning to the words we hear, once they’ve been parsed.
The only morphological limitation to using these suffixes productively is that -ness must be added to adjectives and -less to nouns. As such, there is no possible order between the two: they cannot appear in the same place, which rules out any internal ordering of them, as ‘ordering’ implies structurally parallel elements. In spotlessness, it is not the case that both -less and -ness equally and simultaneously modify spot; rather, -less modifies spot, while -ness modifies not spot, but spotless.
The simplest way to verify that this is so is simply to take some of the words combining both suffixes and reverse the suffixes. You will find very quickly that this is not possible in either direction. If there were any kind of internal ordering rule going on here, you would expect that one order always won out, which is not the case:
-lessness => -nessless (base word is a noun)
hopelessness => *hopenessless
helplessness => *helpnessless
-nessless => -lessness (base word is an adjective)
weaknessless => *weaklessness
timelinessless => *timelilessness2
1 I’m ignoring here the humorous broadening of -ness to be used with just about any noun. Things like houseness or foreheadness do exist and are used, but they’re a different kettle of fish not directly related to this question.
2 The root word here is of course time, which is a noun; but the derivational base to which -ness is added is timely, which is a derived adjective just like timeless would be. (-ly is most commonly used to derive adverbs from adjectives, but it can also be used to derive adjectives from a variety of sources: timely, comely, gainly, etc.)