On osm there is no fixed list of tags, anyone can just start to use any new tags. Maybe also document it in the wiki. In this case, I would recommend this tagging:

amenity=waste_basket
waste=flags

There is already one mapped this way: https://www.openstreetmap.org/node/10969833780

Well, it’s OpenStreetMap, you can basically tag anything. Although I’ve never seen something like a dedicated flag disposal here in Europe, you could combine amenity=waste_basket + waste=flags.

waste=flags is only used twice to this date, however. See taginfo.

How this data is used, however, is up to the renderers/data consumers.