I actually do not think that there is a brand of football for Flick. What he is is that he is very pragmatic and he usually brings players and staff together.
It was just great how fast he managed to make the changes after he came in charge midseason. He never really had a proper preparation time during his time for Bayern because of the time he came in and than the Covid time and the extra competitions.
After Ancelotti and Kovac with their hero football ideas that did not match to the Bayern squad (Ancelotti might be great for Real - he was not really for Bayern) he got the positional play that players remembered from the times with Pep back. How he could do that this fast: He put Müller back to his no. 10 position after that Coutinho stunt because the club could not get a winger and got that prestigious expensive ex-EPL-star... and made him his right hand on the pitch who often even participated in staff meetings, Kimmich from right back into central midfield, Alaba from left back to central defender - at the end he had an axis with players from the time with Pep that (especially Müller and Alaba) were able to command the team and the new ones around. He implemented a very good pressing. (We relied more on the pressing working well as defensive mechanism than on holding the ball).
In the following months we only had problems when parts of this axis were missing or substituted - or after Corona came and we got even more used to the loud commands - when it was snowing or fans were loud from outside the stadium and there were problems with the accoustic.
Flick always looks that his team is fit and tries to have very good connections with everybody in the team and the staff. When he left half of the staff that was there before he came left, too - even Hermann Gerland who was Bayern's amateur coach for 2 decades and assistant coach with van Gaal, Pep, Ancelotti, Jupp and Flick. Tapalovic, who was about 12 or 13 years Neuer's goalkeeper coach until he had problems with Nagelsmann, was often used as additional assistant coach from Flick. He and Markus Sorg are told to come to Barcelona as assistant coach with him.
For me it will get interesting to watch Barcelona again - how he e.g. manages to get Lewy into play better than Xavi did.