As you can see Minecon capes don't work with custom skins that you import into the game.
Additional information by Auldrick:
The cape referred to in this report is the Founder's Cape on the Capes tab of the Profile. If you try to add it to a skin that you imported, no change is visible. Either the cape is applied but is invisible, or the attempt to apply it is rejected without an error message. (There's no way to know which is true.)
There is a skin pack in the Marketplace named Minecon 2016 Skin Pack. If you download it, it appears on the Classic Skins tab, in the Owned list. The skins in that pack all have a Minecon 2016 cape, so there is a potential for confusion about whether this bug is meant to apply to that pack. It isn't. The capes in that pack are implemented differently and do not appear on the Capes tab of the Profile.