Is it legitimate for people who are being taxed without direct representation to start a revolution?

Answer: Yes

Explanation:

I mean, The United States did it, and I'm assuming that is what the question is referring too.

America was thousands of miles from Britain, and had no power over what happened to them. They held no representatives in parliament, so they had no control over what happened to them. I think it is completely sensible for the colonies to be upset over that, enough so to throw a revolution.