"The clothing's pockets"
Translation:Les poches des vêtements
Seeing as both of you have a higher level in French that I do, I suspect you've both figured this out by now. But for the benefit of others who may have the same question, "des poches des vêtements" means "pockets of the clothing/clothes" whereas "les poches des vêtements" means "the pockets of the clothing/clothes."
No, it doesn't work. With a possessive, like we have here, the "possessed" object is definite. It is "the pockets of the clothing," as opposed to pockets of something else. "The clothing's pockets" refers to all the pockets of the clothing. If we were referring just to some pockets, we would have to add "some of" to the beginning of the phrase.