There is the mute button, just use it!
Seriously, it's so useful. In my last game I played terribly. I was forced into mid Annie, that I don't play, against a skilled Zed who capitalised on every mistake I made. I died a lot, and of course of my jungler started flaming instantly. I'm the type of player who hates arguements, and I tend to tilt a lot, especially if my teammates point out the obvious things to me. Soon the guy started accusing me in all chat that I intentionally feed, and that's when I pressed the mute button. I still had problems, I still couldn't fight the enemy Zed, but I started catching up and feeling more and more in control of the game, eventually getting kills in teamfights. I got calm and started encouraging the team that we are coming back. I only realised that I muted Xin, when the enemy J4 started defending me in all chat. I realised that, I was ready to leave the game (though I never do that) because of my feeding and the raging, and by the end I felt happy and joked around about getting my first kill at 26 minutes. Mute won the game for me. Also if any of you who read this, if someone on your team is feeding, flaming him won't help at all. He is already having a hard time trying not to get dived again, if you are pointing out how worthless he is, he will lose focus even more. And if you die because you weren't paying attention to the game while typing "report XY", you deserve a special badge that shouldn't disappear like the honor crests.