Well I know you can’t record someone else content and then rebroadcast it without permission from the content creator.
Thats why VODs exist and Partnered Twitch streamers can optionally lock those to sub only. Some streamers take their content and post to YouTube at their own discretion.
I’m fairly sure what you want to do is against the Twitch TOS, but I’ m sure Twitch Legal or someone else on this forum has the answer.
But anywho, you’ll be doubleing the number of ads, as Twitch player will play ads and then your system will run ads, I don’t think you have a wise business plan here and I fairly sure it’s not allowed.