If you're changing uniforms because you identify more with a different one (e.g. you wear a Navy uniform, but have spent your entire career in Air Force units) that's one thing, but if you want to change in an effort to affect your postings (e.g. if I have an Air Force uniform, they'll send me to an Air Force base), then you may be disappointed. In the current climate, it simply doesn't work that way.
I had a young steward working for me years ago (before stewards were deemed a "hard-sea" trade) about five years after we transitioned from CF green to DEU. Everyone in the purple trades were asked which uniform they would prefer. On his request form for Air Force DEU, he had specifically written, "because I never again want to be posted to a ship." I was his Divisional Officer in a ship at the time. Obviously, his choice of uniform didn't do him any good. And now, all stewards wear Navy DEU...
In answer to your question, changing uniforms starts and end with a request to your career manager. They have quotas they have to maintain with respect to uniform distribution (although it is beyond me why, since uniform is not supposed to affect posting) and it goes from there.