According to the form of such a flag is a flag suit knights Becella,

Who were knights Becella? And what would their flag doing in Hilandar?


so I do not think the car was used as its logo.
Why then are almost exclusively the role of the army as a military unit flags.
Car if you had it should be imperial banner that is repeated Entry Content hump.

He was used as logo? Sorry I dont get you?
You want to say he didnt use it as his personal banner? Could be. In monastery Hilandar there are two flags held to belong to Tsar Dušan or his units.

Anyway in Middle Ages all flags were military flags, except Church ones. Flags were worn during battles, royal entries, parades etc or they were put on castles and fortified towns. There was no concpet of flag as represent of nation.