So for toxic people, the whole "Mute, Report, Move On" is usually the best method of dealing with them. More often than not, they're looking for an argument and anyone else to blame other than themselves. Sure people make mistakes here and there, however there's no need to flame and cast them in a bad light. You'll often find that if you say nothing, they will simply move on to the next person that will. There's the occasional person that will ping spam and get ridiculous with it to the point of watching your every move while AFK'ing, but they are the rare exception. Usually remaining silent is more productive than engaging in conversation with them. There's a saying that's been around for millenniums, most famous iterations are from George Carlin or Mark Twain:
"Never argue with stupid people, they will drag you down to their level and then beat you with experience."
Most people who are flaming lack the emotional intelligence to see that it's harming others, have a narcissistic personality issue (i.e. "I'm perfect and everyone else sucks, it's never my problem regardless of hard facts"), or have a sadistic pleasure they partake in by doing so (i.e. trolling). That being said, there's always productive ways to communicate with individuals. If your jungler flames you for whiffing an E on Viktor during a gank and they died from the enemy being able to retaliate before killing them, you can always apologize and sympathize with them with something along the lines of: "Sorry! We'll get 'em next time I slipped up and messed up my E my bad." They'll likely continue flaming you anyways, at which point mute them. At that point, you've made it clear you've acknowledged their complaint and validated it for them, so there's realistically nothing else to do.
You're correct - intervening often makes it worse, especially if someone is emotionally upset and looking to vent. If they're looking to place blame they likely don't want any criticism themselves, so it's a touchy area and a double standard they're placing down; further reinforcing that they only want to argue rather than communicate as a team towards a common goal. Mute those people quickly to avoid getting too hot-headed about it and giving yourself unneeded anxiety (as well as preventing you from flaming back and being punished yourself), report them after the game if you feel it was warranted, and move on to the next one (or take a short break to cool off, get your bearings back together, and ensure you don't end up with them again).
