We all did (for most still do) it.
Asking our teammates and enemies to report X person.
If you look through the boards, go in a game, ..., you'll see a lot of people doing it.
But it's NOT ALLOWED.
If you read the summoners code, terms of agreement and all those things, it will be told that it's not allowed. (ofcourse no one reads that, (neither did I but shhh))
If you ask to report someone it WON'T HELP. 1 report or 4 reports is no (or a very minor) difference.
So why would you even do it?
Furthermore, it will just increase toxicity for the remaining time of the game.
Since the person you want to be reported 9 times, will be even more angry.
It's very frustrating when someone flames, the best thing to do is just mute him and report after.
I normally say 1 or 2 things, (nice ofcourse) but if the flame is too heavy, I mute.
I just wanted to put that out here, since not a lot of people seem to understand that it's also toxic.