Brevity is a noun, is it not? So, ambiguous, being an adjective, should be able to modify it, correct? That was the first thought I had regarding the subject, but for some reason it just doesn't sound quite right. In the past, that's normally been a good indicator to me that something in my writing isn't quite right. Is there actually something wrong or am I just slightly paranoid?
Noam Chomsky’s famous example ‘Colorless green ideas sleep furiously’ shows that a clause doesn’t have to make sense in order to be grammatical. Some 85 years previously, Lewis Carroll had shown much the same sort of thing when he wrote:
'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.
Similarly, to say that someone desires ambiguous brevity is also grammatical. Whether it makes sense is another matter.
To quote another answer,
There can be no question whether the sentence is grammatical: it is. That doesn’t mean it’s sensible. Colorless green dreams resting furiously is grammatical, too — and nonsense.
The question is not whether the phrase ambiguous brevity is grammatical, but rather whether it is semantically sound. Does it make sense?
It could indeed make sense, depending on the context1. If you have shortened something so much that its meaning is no longer clear, then ambiguous brevity would probably be an admirably short way of describing that. See this question.
1 I've lost count of how many times I've written that.