It was never an official flag, it flew only one day and was interred with Brigham in his casket, and described by only one man. But it represents the pioneer era, and seems more fitting for July 24th than the US flag. Deseret flag, Flag of the Kingdom of God, Banner of Freedom...
Here is an article on the various iterations of the flag:
https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1653&context=byusq