Sisko did not have old flag friends of note.
I would consider Admiral Leyton a friend of note, particularly seeing as how Leyton took credit for turning Sisko onto the command track and the fact that Leyton was Chief of Operations in all of Starfleet.
And while they might not have been best chums, I would say that Sisko was certainly friends with Admiral Ross, who at times seemed to be practically running the war from DS9 on his own...with Sisko's and Martoks help. (that warrants a discussion in its own right. Where was the rest of Starfleet command during the war? Sitting on their hands back on Earth? You've one three star admiral calling all the shots on the front line, with what appears to be practically no backup from command.)
Sisko also seemed well acquainted with numerous captains throughout the fleet, given their involvement during the war.
Realistically, it would make sense to have a working relationships with those above your pay grade as well as the fellow senior officers within your specific fleet assignment. While advancement is ideally merit based, there will always be those who move up the ranks because of who they know.
And given that Starfleet Command and Starfleet Acadmy are right next door to each other, it seems likely that there would be plenty of opportunity for cadets to meet higher ranking officers. As Admiral Hanson said, he took note of Picard during a race in his freshman year at the academy. So I would imagine that any career minded cadet would make a serious effort to gain the attention of as many captains and admirals as possible during their time at the Academy in order to build relationships that might help their careers down the road.
While it might be slightly off putting, there is something to be said for accumulating favors among those that have more power than yourself.