As a Braum player, the key is trying to avoid his q. Keep your minions between yourself and Braum. Get 1 stack of his passive on you, back off and let it time out. And when you see him fully commit, move because that may mean he is gonna use his ult (or their jungler is near by).
With Thresh, try to land your hooks on him to draw him in so the adc can pepper him (or draw him off them). Build tanky as well (due to Thresh's passive, he can be very beefy) that way Braum can't make a quick meal of you. Use the shield from the Lantern and the slow from your ring.
I play Braum a lot, so i know some ways around him. Best scenario with facing Braum is getting him alone. Force him away from his ADC and he can be an easy target for the jungler. I hope this was of some help. I don't really play Thresh a lot and am usually Lulu, Karma, or Taric against Braum.