I'm not sure if this is a bug or if I am doing something wrong.

So I am at the quest where I have to trap the Dragon at Dragonsreach.

I trapped the dragon, and talked to him. He promised me to fly me to skuldafn, where I should find the portal to sonvgarde.

The only problems is when I tell the guard to free him, I see the quest changing telling me to talk to the dragon. But as soon as he is released the other NPC's around start attacking the dragon. I thought this was supposed to happen, so I defeated the dragon. He then started to idle for a few seconds and then had full life again. And it started all over.

I'm pretty sure I'm supposed to be able to talk to him after he is released, but it's just not happening with people attacking him and him breathing fire at me.

Can anyone help?

Sounds like a bug of some sort.
Try reloading a previous save and trying again.

Oh wait have you tried talking to him yet?
Before freeing him you need to talk him.

Talk to the dragon after a good save. Be sure to scroll the list of the dialogue. Go upstairs to the guard and ask him to release it. Then quickly go down and talk to the dragon. Then you'll see you climbing on it and flying away. If there is a problem reload and avoid a sentence in the dialogue (sorry but I don't remember which one but try again). I think also that as soon as you return to the dragon, tell him something like (I'm ready) or (bring me ....). If you are quick enough the other guard won't have time to shout at him. Ignore him...