Tips from an NA Silver Jungler (a.k.a. the first target of flaming):
If someone is flaming you or anyone else on your team, mute them. Something I do is I tell my team to mute the player as well to help me and my team avoid tilt.
Try to avoid typing in chat. I find I tilt less when I type less. So don't use chat unless you need to communicate something more complex that's important, like telling your team to push waves then take baron, or to prep an objective before it comes up.
USE PINGS NOT YOUR KEYBOARD.
If someone is just complaining in chat, mute them, it can and will put you on tilt.
Do NOT send even one even slightly sarcastic or flamey message in chat. If you do it once, you will do it more.
Think about how to win the game and focus less on individual players. Playing support and your ADC is a lost cause (gets caught out of position constantly despite warnings, takes dumb fights repeatedly)? Roam, do not go back to lane, invest resources into deep warding the enemy jungle and ganking other lanes. Keep in mind everyone makes mistakes once or twice and that doesn't mean you should just give up, it's just when they don't learn. Mid/Top and your jungler won't gank? Roam/TP gank if you can't win your lane. Keep in mind there are lanes your jungler will have trouble ganking, and if you want a gank, let them push and freeze the wave near your tower. ADC and your support keeps getting caught? Simply ask them to stand behind you, just let them push and let you you farm so you can scale. Jungler and you're behind? Play around a strong/winning lane. When your laner is pushed tower, in most situations your laners will get to you faster than theirs if you find/fight the other jungler. Use this safety to get wards into their jungle and when they gank the opposite side of the map you're on, invade their jungle/set up vision. You can also just farm it out if the champion allows it.