It’d be possible to start the process in Twitch chat, but it would move to a separate webpage for payment processing (something you’d set up on your own server) as well as if there is any personal information being exchange (for the security of the user).
So, as long as your bot has the ability to connect to a business that offers food delivery (maybe in a similar vein to TreatStream), then I suppose you could implement a ‘chat’ function to start the order, but Twitch itself would only offer the chat portion, everything else beyond would be in your court.
I’m not sure if there are any restrictions on Twitch’s side from setting something like this up, something like this is not something I’ve ever looked at to be honest.