I did a Goggle Image search 34th Texas Cavalry and came up with this site. I would assume the one star on a blue field flag was their regimental flag.

George Martin

http://images.google.com/imgres?imgurl=http://gen.1starnet.com/civilwar/34cvmain.htg/bonnieblue.gif&imgrefurl=http://gen.1starnet.com/civilwar/34cvmain.htm&usg=__KgnHO11u2gS8nsxL152BoXeAoT0=&h=50&w=68&sz=9&hl=en&start=34&um=1&tbnid=idXXU05rx7TWWM:&tbnh=49&tbnw=67&prev=/images%3Fq%3D34th%2BTexas%2BCavalry%26ndsp%3D18%26hl%3Den%26client%3Dsafari%26rls%3Den%26sa%3DN%26start%3D18%26um%3D1