二度と来るかこんな病院!!
The character is an old man who is angry. He's not going to go in that hospital once again. Why doesn't he say 来ない?
二度と来るかこんな病院!!
The character is an old man who is angry. He's not going to go in that hospital once again. Why doesn't he say 来ない?
This か is a question marker, and the sentence is a rhetorical question to emphasize the sentence. It literally means "Will I come", but actually means "I'll never come (again)".
This is one of the common usages of か (or かよ). Similar examples: