You DO NOT want to wear your inflatable under your parka! Unless you take the parka off first, before inflating, there would be no room for the air bladders to inflate. They are generally meant to be worn outside of all clothing.

The bladders expand and get very large when inflated. That's why the inflatable vest have so much more buoyancy than conventional PFDs. If you were to inflate it under a parka, the bladder wouldn't have room to inflate properly. It also would probably also severely constrict your breathing.