What are the flags beside the US flag at Trump's inauguration (marked by an arrow in the picture below)?
It's the Betsy Ross flag.
The first documented usage of this flag was in 1792. The flag features 13 stars to represent the original 13 colonies with the stars arranged in a circle.
It is the early version of the American flag. Check the below image for more info. Note on extreme left and extreme right doesn't seem to refer to flags.