1: As much as I hate saying it, /mute exists for a reason. You will unfortunately come across jerks playing this game, but that is why /mute exists. Just mute them, report, and move on. Dwelling on negativity will make you hate everything.
2: If someone is flaming you during a game, why the hell would you add them to your FL? This is common sense. What good do you think would come from adding someone who was flaming during a game? I'm not trying to be rude but this makes no sense to me why anyone would add someone right after a game if they were being an assbag. If this was someone you had way before and they randomly sent that to you, well just remove them and send a support ticket with the summoner name and a screen shot. If not this just looks like you set yourself up to be chewed out.
Most of us in the community know there are plenty of toxic people that play this game. But toxic people exist everywhere. Even at work, home, and with friends. But there are also plenty of positive people who play the game. It's just the toxic players are more vocal than the positive ones. If you're going to keep sitting here feeling "woe is me" then all I can say is tough luck. People suck, but dont let them ruin anything for you. You play the game for yourself and how to want to. If someone is a problem then deal with it using the appropriate steps and move on (mute, report, and block can be your best friends dealing with these people).
I'm sorry you had to deal with flamers, but from someone who's been playing the game for a long time this will never truly go away. So cheer up and play for yourself. Don't drag yourself down to their level or respond with how they want you to. Just play and have fun.
Good luck!