The very concept of kinetic energy storage is already in conflict with the laws of physics, which makes this one extra hard to replicate in real life.
The Editors of Encyclopædia Britannica explain that a body in space has kinetic energy if — and only if — it is in motion, meaning that kinetic energy cannot be stopped in place or held inside of a vessel for reuse, much less inside of a thin layer of clothing.
However, there are a number of ways that kinetic energy sustained from a blow could be redirected and redistributed by a piece of clothing in order to protect the wearer, similar to the way that a helmets and shin guards protect the brains and legs of athletes. A Google patents search reveals there are a few sportswear manufacturers working on this technology right now.
Most notably, a company called Blue Design Limited has filed multiple patents for thin, soft materials that would theoretically provide similar protection from direct hits by absorbing and dispelling kinetic energy across a wide surface area.
Again, a patent does not mean that you'll see this tech in sportswear stores any time soon (companies patent things all the time even if they're never used), but we can keep admiring the ingenious craftsmanship of the suits from "Black Panther" in the meantime.