Is there any such Kriegsmarine rank as a flag lieutenant - I don't think there is. I think that flag lieutenant is a Royal Navy rank only.
I have queried the role actually played by the up to 80 staff officers on Lutjens staff in several other threads, noting that the difficulty in answering this question is compounded by the fact that none of them survived.
The most senior staff officer was Captain Harald Netzbrandt (former captain of Gneisenau), followed by Commander Paul Ascher (former gunnery officer on the Graf Spee). Presumably Netzbrandt would perform the role of flag lieutenant.
''Give me a Ping and one Ping only'' - Sean Connery.