No, Amazon is a publicly held company, not solely Bezos' property (I doubt his board would even let him do the same thing).
Chick-Fil-A is for all intents and purposes is the "personal money" of the owners, so I see no difference in what someone does with his money or his property.
I'm fine with the boycott. I don't support it, but I respect it.
What I'm not fine is this.
>not allowing expansion into communities that disagree with his stance
If a local government denies building permits to a business because it disagrees with the owner's speech, that is a blatant first amendment violation. Far more knowledgeable people than myself have said the same thing. I really doubt the lawyers for whatever municipality plans on banning them will allow that to happen.
If the people of a local community don't want Chick-Fil-A there, they won't patronize it. Chik-Fil-A's market research will probably find that out and they won't build there.
As for rights, try to keep in mind the key issue here is a debate on a specific right as well. What people are debating is changing the law, changing your rights. If local governments feel a certain right or something they desire to be considered a right is being infringed on or threatened by a company, then it's no longer so black and white.
Besides, it's not like people are saying the Chick-Fil-A president can't say what he said. The story here is that a lot of people are deeply unimpressed with his statement, and are effectively enacting a de facto boycott (not allowing expansion into communities that disagree with his stance).
It's perfectly fine for this to be discussed, and besides you possibly not identifying with the complainants (as you point out in another comment here), I don't see why you object to it. (Note that I am mainly responding to the parent comment from another user: "I find it odd that what people do with their own money gets so much attention".)