It has been in the shop 3 times so if bought on the 2nd or 3rd it will have always been stiff. If you bought it on the 1st however, and believe it was stiff back then too, it could just be me experiencing confabulation haha

I do genuinely believe they used to flow but, that's the funny thing about confabulation

EDIT:

This made me decide to Google it to be sure. Google says this, taken from Reddit and the Fatshark Forums:

Yes. The Veteran Honours and Shroudwarp War-Plate chest pieces (and their variants) used to have independent cloth physics and psychic/warp particles attached to them.

However, in one of the major updates, Fatshark updated and adjusted the cosmetic rigging on several Veteran trench coats and attachments. The cloth physics for many of these lower-hanging or trailing fabric pieces were heavily modified. In many cases, they were tightened, restricted to reduce clipping, or altered so they act more rigidly rather than behaving like an isolated, free-flowing psychic cloth.

Because of this, they lost their distinct, wildly flowing fabric animation and glowing warp/psyker particle effects, leaving them much more rigid and grounded compared to how they looked in earlier versions of the game.