What was Johnny's condition after the fire in The Outsiders?

Johnny is injured so badly that he succumbs to his injuries and dies.

Of the three boys who were injured in the fire, Johnny was in the worst condition. He was badly burned when part of the barn fell on him. Pony was told about his injuries by the man who took him to the hospital, who Pony initially thought was a schoolteacher. 

He burned one arm pretty badly, though, trying to drag the other kid out the window. Johnny, well, I don't know about him. A piece of timber caught him across the back — he might have a broken back, and he was burned pretty severely (Chapter 6).

At the hospital, Pony sees Johnny and Dally brought in on stretchers. Dally is cursing out the nurses, but Johnny is unconscious. His face is not burned, but his injuries are worse than they appear. Johnny looks “very pale and still and sort of sick.”

When they finally get an update on Johnny's condition, it turns out to be as bad or worse than they had expected:

He was in critical condition. His back had been broken when that piece of timber fell on him. He was in severe shock and suffering from third-degree burns. They were doing everything they could to ease the pain, although since his back was broken he couldn't even feel the burns below his waist (Chapter 7).

There is nothing that can be done for Johnny. The greasers are able to visit him, even though they are not family, because the doctors realize they are Johnny's real family. Johnny refuses to see his mother.

After the rumble, Pony and Dally go back to visit Johnny.  They are just in time. Johnny tells Pony to stay gold and dies. Dally runs off, horrified and plagued with grief. He was not as badly injured as Johnny, but he later robs a grocery store and runs at the cops, essentially committing suicide.