"Have no intention" is not a phrase that you would use in a friendly way. It's not hostile or unfriendly by itself, but it is a pretty formal way of speaking. It is almost a defiant word, denying that you intend to do something (bad or hurtful) that someone has said that you are going to do. It says "I deny that I am going to do what you have just said I will do," or (and this is different) "I am not going to do what you have just ordered or demanded that I do." "I don't (or, much more likely "didn't") mean to hurt your feelings" is usually an apologetic statement, by which you are saying that you feel bad that you did something that caused the other person to feel sad or demeaned somehow. It is a very personal statement, from one person to another. The "no intention" statement does not suggest a close personal relationship between the two people.. I can't really think of a situation when someone would say "I'm not going to hurt your feelings." Hurt feelings are a result, a consequence, of something that someone does. "To hurt someone's feelings" is not -- itself-- something that one does. In a situation like this, they really would say "I'm not going to [do whatever it is that would cause the hurt feelings, such as "insult your family" or "tell you that you are dumb."]"

All three are future tense and all sort of mean the same thing. Also, the phrase "I didn't mean to hurt you feelings" is used when you've accidentally insulted someone. Hope this helps :)

I'd agree with Carlos that 'I have no intention' is quite cold and formal, and has the effect of 'distancing' you from the other person. It isn't the appropriate register for talking to a friend about feelings.