Please, explain what it is you want to say. We understand fly into a rage; we just don't understand what you are asking us to do for you. You said you wanted to know the opposite of fly into a rage using the word fly. I can't think of anything because the question of an opposite with the same word makes no sense in English.
People don't stay in a rage for ever. Eventually they calm down. Perhaps this is what you mean by "the opposite", but this notion cannot be expressed with the verb "to fly". "Out of" is the opposite of "into", but we don't say *I flew out of a rage."
Could I use only one word "fly" to indicate "fly into a rage" ?
For example : A woman was choking, she was trying to get a small object out from her throat, finally, she flew (into a rage) to get it out of her mouth.
Is it right if I sing "flew" in that sentence like that ?