What does it mean to have a British flag over the AA airborne patch/tab on the left arm?

I got a chance to see someone speak at a brief. The person had a British flag over their AA patch/tab. It had me thinking...does the 82nd ABN division have other other fractions of the division a part of foreign armies? I maybe confused about it but if that was the case I definitely think that's cool for a specific unit to be stretched across multiple armies for multiple governments. Is there any other unit like that. If that's not the case someone please clarify what a British flag over the AA airborne patch on the left arm means. As for why I didn't ask the man himself...My mind was prioritizing information given so think question wasn't a necessity. It was more of me just being inquisitive about something I've never seen before. I made a note of it and kept it moving.