Having looked at the SCV listing and biographic sketch for Brack Masterson, I think its so much hocum and fanciful story telling.
http://assets.luginbuel.com/genealogy/documents//Benton%20County%20Arkansas%20Confederates.pdf (page 168)
A 12 year old did not ride to Lawrence. He may have met Quantrill sometime (right place, family with right connections, right time) but he was not part of the unit. Young adolescent imagination developed memory over years. The second claim that Bat Masterson was his brother is a flat out non-starter. Braxton did have a younger brother, William Wesley Masterson who died at Waverly MO in Dec 1871. There is no connection at all of the family to Bartholemew William Barclay Masterson gunfighter/author who died in New York in 1921.
There appears to be no military record of service during or after the civil war for him. His older brothers did serve in various units.
He would not be the first nor last to invent a military service history for himself.