Is somebody flaming you? MUTE Them.
Don't flame them back, start an arguement or provoke them, just MUTE them.
"Well why should I mute some fgt, I can flame him back and make him feel bad"
-Well, there's 3 good reasons why you should mute someone.
1) You'll be much more focused, and relaxed. -This doesn't necessarily mean that you'll play better an win every game, but these two factors; focus and relaxation, are quite important regarding your mental state, your decisions will probably be better and you'll most likely have a better game.
This doesn't mean you'll automatically win every game and go 20/0 in your lane, but you will play better.
Went off topic...
2) The flamer might overall play better. -While that's not ALWAYS the case (it is most of the time, though), if you don't give the flamer attention, he'll eventually keep quiet (That's how, again, it works most of the time), probably being more focused as well, and have a better game.
3) Instead of typing, you'd do something USEFUL! -Although communication through typing IS good; It's also a flaw, remember that, while you are typing, you can't do anything, your champion has a will of its own; and by that I mean, it's as if you're AFK.
So, instead of unnecessary typing, play the game, do useful stuff, and win.
Just a daily reminder that you should mute people (esp. flamers) and the game will most likely go better.