Has Trump the power to close down social media platforms?

He does - in his own mind at least - under the Emergency Powers Act.  It is not clear how stifling Freedom of Expression would fare under court scrutiny or how stopping the incessant criticism would cease if he shut down Twitter or Facebook.  It is also, not clear how the Emergency Powers Act could be involved just because the orange twit is unhappy with what is being said about about him.

No, tiny-twerp (5'10" pretending to be taller) spoiled-brat toddler-stuck Trump does not have the power, Londo Mol.  It is just more tantrum-throwing hot air.

He wants to regulate them according to existing FCC protocol. Yes, he is well within his rights to use executive order to get the FCC to enforce existing law. And most importantly he should regulate them to preserve democracy and free speech. Social networking sites can't just censor free speech if they want to be legal platforms and not publishers. Once they start editorializing and limiting free speech, they become publishers and lose legal protections that platforms receive.

Well, FDR did muzzle the media during WWII, and we are currently at war with an internal enemy.....Liberals.....so I guess that Trump can do the same thing.

When doesn't he BLOW hot air?

He does not have power over private companies.

just more of trumps rants and ramblings

Yes. All over the world. Nobody will be able to see them any more, even in countries he hasn't heard of and couldn't spell.

In theory, he could shut them down with a Presidential decree.  The social media platforms would then go to the courts and have the decree annulled.  By the time that's all over, the elections will have passed and Trump will have made himself look even more of an idiot.

Of course not.  Fact-checking is not a denial of free speech, it's just more speech!  But Trump's fans love the 'tough guy' approach.