I think Sword got the flags confused. This was the 13th USCT's first fight - they had been building and guarding the railroad from Kingston Springs to Johnsonville, TN for most of their career and these flags were probably the only set of colors they ever received as a unit.
If West Point's list states "regimental flag" then this should be the blue flag with possibly the US coat of arms in the center (unless David Bowser did this flag as he did for the 12th USCT)in which case it would have something different.
US colros with nice slogans can also be deemed beautiful colors as well - I have seen many such descriptions.
I wish this flag was still around for it would be easier for us all then.