Noun
the rank of a flag officer
Source: WordNetAlso, 24 Captains were promoted to the Flag Rank of Commodore and 19 Commodores were promoted to the Flag Rank of Rear Admiral. Source: Internet
For example, it was not until 2001 that the UK made "commodore" a "flag rank", and changed the shoulder rank insignia (although not the cuff rings) of the higher ranking admirals accordingly. Source: Internet
However, this was considered an awkward title and the one-star flag rank was renamed a few months later to its current title of rear admiral (lower half), later abbreviated by the U.S. Navy and U.S. Coast Guard as RDML. Source: Internet