Unfortunately, for Minecraft Java Edition, there are no skins that will automatically incorporate a cape. However, in Bedrock Edition, there are some skin packs that come with capes included.

Minecraft capes were introduced in the game in 2010, and ever since, a handful of designs have been released during various events.

How to earn the Yearn Cape Upgrade Minecraft to the latest version (Bedrock or Java Edition). Access the Movie Live Event from the main menu (Bedrock) or join the event server (Java).

Capes have yet to be added to Minecraft on console. You can already fly in the game's Creative mode, where mobs are turned off and you have an unlimited palette of tools.