Because damp isn't the same as wet. Sometimes something damp might just feel cold to the touch. It doesn't have to be wet enough to actually mix with dust to make a sort of mushy mess (it would never be called "mud").

Retired English Teacher
Ask the gardening shoes that I used to leave in my garden shed in the winter months. They managed it.
Typoman - writer of rongs
Because damp isn't the same as wet. Sometimes something damp might just feel cold to the touch. It doesn't have to be wet enough to actually mix with dust to make a sort of mushy mess (it would never be called "mud").
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
A google search returns several results for each of "damp and dusty" and "dusty and damp". Oddly enough, the Corpus of Contemporary American English seems to contain neither. Perhaps I'm using the CoCA wrong.
I was surprised that CoCA didn't come up with anything. Ngram, however, gives many hits for "damp and dusty" but nowhere near as many for "dusty and damp".
However, bear in mind that certain words not appearing many times in a string on either CoCA or Ngram doesn't mean they don't provide a grammatical sentence when used. Imagine that I have a shiny small car that's red and green with purple spots. It's perfectly reasonable for me to say "I've got a small, shiny, red and green and purple-spotted car". If you put "small, shiny, red and green and purple-spotted" into CoCA, I doubt you'd get any results at all. That doesn't mean there's anything wrong with my sentence.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.