It might not fall outside the law, but it definitely falls outside common sense.
You're right, it might not fall outside the law. The only way, in this case, that it is likely to fall outside the law is if he violates an ordinance on outdoor burning. "Protected free speech" itself has limitations. It is legal for me to say "The President flagellates frogs." It is legal for me to put my slogan on a sign and walk around with it. It is not legal for me to spray paint my slogan on public property, or on private property which I do not have permission to alter.
And you are right again, burning a Quran is not a sensible thing to do. It is an expression of bigotry and contempt which serves only to inflame passions.
To me his actions are no different from "satisfy all my demands or I'll blow up this plane". So that definitely falls out of free speech. He's using his supposed "free speech rights" to negotiate something. That sounds a lot more like blackmailing than free speech to me.
It might be an attempt at blackmail, since he has publicly announced that he would consider certain quid pro quos to be a "sign from God," and since there are definitely some for whom the burning of this book would be an undesirable outcome. I hadn't thought of it, but perhaps a case could be made on that basis.
Certainly the thing being threatened doesn't have to be illegal for the situation as a whole to be blackmail. The person threatening to reveal facts about David Letterman's affair unless he was paid a sum of money was convicted of blackmail, and "revealing facts about David Letterman's affair" is not illegal.
It's possible that Jones has crossed a line here which would make further threats unwise...
On the other hand, I'm not sure it would constitute blackmail. Perhaps an element of secrecy is necessary for the crime of blackmail. The threat in this case might be considered simply a negotiating tactic. When the owner of a sports team threatens to take his team to another city unless he gets certain concessions ("Build me a stadium!") they're not charged with a crime. When people boycott a business attempting to bring about change, they're not charged either.
ETA: I think we're more properly talking about "extortion" here; "blackmail" seems to involve the threat to reveal information, while "extortion" includes other threats.
Obviously, I'm not a lawyer. I'm just thinking out loud here; I really don't know.