Feedipedia is the best place to check for stuff like this - as to tannins - 99% of the sorghum in the USA is tannin-free cultivars.
http://www.feedipedia.org/node/224
http://www.feedipedia.org/node/224
Read the above and come to your own opinion - my take from the article is that high-tannin sorghum isn't particularly good for the birds, but low tannin sorghum is a great food.