The best design, in my opinion, is one that will prevent data inconsistency and prevent people from having enough rope to hang themselves.
If you need only one favorite for the parent, perhaps the parent should have a favoriteChildId column.
If you put a column for your favorite flag in a child, you will need to do more work so that two children of the same parent cannot be marked as favorites.
If you suspect that in the future you may have more than one favorite, then, of course, the extra work may be worth it.
Design really depends on the relationship and whether there may be changes in the future to the possibility of different "favorite" relationships.
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