Okay, here’s my experience linking my MLB The Show account to Twitch, told in a casual, blog-style format:
Alright, so I wanted those sweet Twitch drops for MLB The Show. You know, free packs, stubs, all that good stuff. I figured it couldn’t be that hard to link my accounts, right? Famous last words, maybe.

First, I went to the Show website, the one. I logged into my account, the one I use for PlayStation Network, since that’s where I play.
Then I clicked on the head picture icon, and went to “My Account”.
I found where it says “Linked Accounts.” Clicked that.
I Saw the Twitch logo, clicked it. I was prompted to log into my Twitch account. Simple enough, I typed in my username and password, the usual drill.
It asked me to authorize the connection. I clicked to give the ok.
Done! Finally, I went back to the Show Nation website, and it showed my Twitch account as linked. Success!
It wasn’t too bad, just a few clicks and some logging in. Now I can watch other people and earn some rewards. Hope this helps you.