Glenn Dedmondt erroneously called it Company A in his book, "The Flags of Civil War Arkansas." Pelican Publishing, 2009
Ken, there is a review of this book at:
http://books.google.com/books?id=KCAxwqU1oAEC&pg=PA16&lpg=PA16&dq=hot+springs+rifle+company+arkansas+flag&source=bl&ots=rn_JQjJ1-M&sig=lJ80rrBRr6iVx88RDWDJn_tQIOQ&hl=en&ei=Nn20TeuOMeXn0QHkoeHUCQ&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CBgQ6AEwAA#v=onepage&q=hot%20springs%20rifle%20company%20arkansas%20flag&f=false