Same issue for me. On my Twitch settings, it still keeps asking to "Connect" even though on my Bungie.net "Account Linking" settings my Twitch account is linked.
EDIT: Can confirm what DarkDreamer426 said. Go to "https://www.bungie.net/7/en/Codes/Partners" and click on the "CLAIM" button. It errored out a number of times for me. I went into the game and looked under FLAIR -> EMBLEMS -> GENERAL tab and it was now there.