Flag hats are counted as base game vanity items, found in the 150 relic chests. Most other new things are DLC vanity items, found in 2000 relic DLC vanity chests. Some things, like pirate skins, are "premium" DLC vanity items found in 3000 relic vanity chests.
I really hope they start giving you more than one skin at a time. I can't imagine how bad it's going to feel to spend 3000 relics and just get a lousy preset.
edit: or maybe I'm wrong. That's the impression I got from the locked item descriptions. I spent all my relics on DLC gameplay chests, haven't opened any regular vanity chests yet.
double edit: Nope, I'm right. Got all the flag hats and the regular vanity chest returned to "completed". Also, the chest opening for reward chests is extremely broken right now.