Existing items are always a good place to start when thinking about a homebrew item.
In this case, the DMG describes the Animated Shield as a Very Rare item that requires attunement and, as a bonus action, activates to "hover in your space to protect you as if you were wielding it, leaving your hands free" for a full minute. There are no usage restrictions, just the bonus action once per minute, and it doesn't even require proficiency.
It should be fine to keep those mechanics and then reskin the description of how it works to fit your desired "look", with DM approval. For example, we might describe this as not a flying shield, but as a metal gauntlet that can instantly deploy into a shield to block a blow and then retract immediately after. Or we could say it's an "Armor-caster" on your belt that fires out little flying armor plates to intercept attacks.
And if it's not quite what you want, making small alterations to an existing item is usually an easier "sell" to the DM than making up something wholly new. I'm not sure I'd remove the bonus action requirement, though, especially for a monk-barbarian, where your bonus actions are quite valuable every turn (as opposed to, say, a fighter or wizard, where most of the time they probably don't have much to do with their bonus action and waiving that requirement isn't particularly meaningful).
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