Non-nobles (i.e. gentry families) could have coats of arms. The term 'squire' had fallen out of use in its original meaning and by the Mid-15th Century was beginning to be used to denote the gentry class as a whole (like the écuyers in France and the junkers in Germany) and would eventually result in a proliferation of 'country squires' in following centuries.
When Trollope acquired his coat of arms seems to be questionable, but it may have been when he became a life peer (he was granted the barony of La Ferté Macé). As his arms are not conjoined or labelled, it is fairly safe to say they were granted to him and not inherited from his father (unless his father was dead of course).
I've never encountered anyone not an hereditary peer (knight banneret upwards) who had a right to bear a livery standard and a badge. However it was quite normal for any household to have an informal livery, even if that household consisted of just a few servants (like the Pastons for example). Whether Trollope's livery was in use before his defection, or whether he was granted the badge and right to livery once he became a banneret after 2nd St. Albans is open to question. It's quite ironic that his badge was a peacock, given his bragging about the battle. It was not unheard of for new badges granted to be a play on a name, or perhaps an inside joke.
As an officer under Warwick in Calais, he would have borne his own coat of arms if he had it then, or he and the men who defected with him would have all been wearing Warwick's livery, as he was Captain of Calais. It seems likely that Trollope's men would have been re-outfitted with either Henry VI's livery after changing sides at Ludford (they were Royal troops after all), or Somerset's, whose service Trollope appears to have gone into.
So quite literally Trollope's livery might only have been worn by the guy carrying his banner and his valet, or alternatively after 2nd St. Albans Trollope might have had an entire contingent outfitted like that.
Knowing the original source would be helpful, as claims to 'ancient' arms and badges was rife in the 16th-18th Centuries and it is possible that the livery could have been made up long after Trollope's death. That it is just two colours suggests to me that it is probably a genuine 15th Century one though.
Well that's my view for what it's worth. It is a quite striking livery though regardless.
£350 for the four book set... gosh.