I am a real stickler for flag authenticity - if it cannot be documented then I would not use it basically. Reenactors do a good job on uniforms, guns and other stuff but let the flags part of things go slack.
I have consulted for several large reenactments including Mill Springs, Corinth, and Shiloh all of which were maximum effort events. They wanted to be sure that the right flags were on the field - flags correct to that battle. This is the only way to go in my book.
I just checked my files and do not have a file for Co. A of the 16th. If I did I would have been happy to let you know about it.