As you can see Minecon capes don't work with custom skins that you import into the game.
Additional information by @unknown:
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.
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Bug is present in 1.13 released non beta version

Still happening in 1.13 release for Windows 10.

This is not fixed, title is incorrect. Still effects 1.13.0. The Founders Cape was promised to be released in 1.13.0. Why is it not added yet? iPad Pro on iPadOS13.2.

Exactly, the cape dont work and the elytras dissapear!

The elytra becomes like two capes and it is also completely black

Please note that this issue is fixed in the 1.14 beta versions and not in 1.13.

Fix in 1.13.1
Resolved at reporter's request

Gak ada founder cape

Don not founder's cape
This happens on the 1.14.0.1 beta on Windows 10 as well...