Putin has staged terrorist acts against his own citizens before.
Although some of those events look pretty bad at first, there's nonetheless significant criticism of that theory from neutral third parties.
The biggest criticism of it is that the entire conspiracy theory makes no sense, as it revolves around the idea that Putin's FSB bombed its own people to create support for the war in Chechnya. Except that war had already been started by Yeltsin with the full support of all the power structures and Putin's 1999 attack on Chechnya was preceded by the insurrection in Dagestan. There was no need for apartment bombings to get an excuse to engage in military action in Chechnya. The claimed motive just doesn't line up with the actual timings of events.
The second biggest criticism is that the people who suggested the possibility had no evidence for it good enough to stand up in a court.
The third biggest criticism is that whilst the motive of the Kremlin to do this was rather garbled, a Chechen rebel leader had actually said "[they would] set off bombs everywhere", "Russian women and children will pay for the crimes of Russian generals." and that "this will not happen tomorrow, but the day after tomorrow" ..... and two days after he said that, an apartment building was bombed. And after fighting in Dagestan was concluded the bombings stopped.
So you have two possibilities - Islamic extremists bombed the apartment buildings in retaliation for their insurrection being put down. That possibility is a simple one. Or the Russian government engaged in a conspiracy to bomb its own people in a false flag operation. Given the history since 1999 of Islamists blowing shit up, I say ... go with Occam's Razor.