It doesn't seem like it's possible to customize your kit, except for when you are playing or in the main menu (i.e. not between matches). Or am I missing something?
You have a period of time between matches when you can customize your kit and that's when the new map has been selected and the countdown timer hasn't reached zero. I'm talking about the time where you deploy but you cannot move around (only jump, switch weapons or drop boxes).
If you don't deploy, you can hit
square (on PS3 - it's the "reload" button) and go into the customize kit menu.
One thing I've noticed about this is that you can only customize kits that are relevant to the current map. So for instance, you won't be able to customize the
Jet kit when the map is "Operation Métro" (rush) because there are no jets on this level.
If I remember correctly, you can also access this menu when you are dead and haven't respawned yet.