If its a normal game and you have a low tendency to flame others and that you're not feeding but your team is, going into all chat is a fun way to lower your anger (although talking too much will make you lose the game, which might anger you unless you talk so much you forget about the bad game)
Joke around in all chat (refrain from flaming) and just have a convo. Now if your teammates start going into all chat and flaming you/enemy talking negative towards you then you mute everyone. Usually you can hold "decent" convos in all chat.
Talking in all chat takes your mind away from the situation. Sure, you might lose the game by talking in all chat but if your team is already losing really badly cause of bad choices (assuming thats the reason why you are raging) then it doesn't matter.
usually having a good convo in all chat leads to a more relaxed environment.
Also do not make your all-chat comments sound sarcastic LOL..
Now if you are feeding to someone, I say for you to not try to all-chat cause talking to the person you are feeding will make the situation worse (i learn from experience LOL..)
If all goes bad, theres always the /muteall or whatever command input.
You can also /message your friends on league during the game to talk about the situation. Just make sure that the stuff you say to them (especially if its about your teammates) doesn't accidently leak into all chat. Sometimes i mistake all chat for the /reply message lol.