sometimes?

Here's how i see it:

Some understand flag as being exactly like OP describes - if player A flags to player B, A is obliged to take a place lower than B.

Others understand flag as being obligation to not attack. In this way, you could justify that if player A flags to player B, but B is being attacked by C, A could sit tight and wait for player C to kill B, eventually resulting in A getting a higher position than B.
However, in my opinion, this last situation is "flawed". Player B is getting attacked by player C. But when B realizes that his defeat is certain (if he has as little as 1 territory left), he should flag C. Since A has promised not to attack B, B can fight and eventually kill A (even if for instance A has 20 territories and B has 1 when B flags C).
Therefore, A must always get a position lower than B. And thus both views result in the same thing. And my answer to AndyLT's questio will be "yes".

as long as there is no programmed real flag from A to B, vflags are sometimes open for interpretation

in most cases A should take a lower place than B but sometimes B does things in the game that can allow A to "unflag" to B

in theory, we flag for a position, not really to a person

iI forgot to mention there is a good post about flagging in the advisor blog by Vermont

I have a question about flags too:

what do you call these pieces of coloured cloth attacked to the top of a flagpole.
hint: knights and pirates use them.

I have another flag question:

why is it that a white eagle on a white background is the war flag of the french and dutch?