More can be said but for starters here is an amswer I wrote in dialogue with a now-deleted user on the 1999 Apartment Bombings. Most of the "it was an FSB False Flag operation" theories specifically are about the reports of discovered Hexogen (an explosive) at a "training exercise" at a Ryazan apartment building (unlike two other apartment buildings in Moscow that month no explosion occurred and no one was actually killed). All three apartment incidents occurred during a wave of bombings, mostly truck bombings, in the Northern Caucasus and Moscow.

It's really very difficult to say much more than this. Official sources say one thing while political opponents of Putin (who are not all reliable narrators) blame the FSB and Putin, but evidence that could lead to a better answer either way was very quickly destroyed and no further meaningful investigations were possible.