Ken is exactly right, the only known flags for the 16th are national flags. Although there is not a flag around to show for it, the 16th Louisiana would have carried a Hardee Pattern Flag from roughly the August 1862 to late 1863. They were part of Hardee's Corps from August - December 1863 and it is confirmed at Perryville, Murfreesboro and Missionary Ridge (from enemy descriptions they fought against) that the brigade the 16th Louisiana was in (Adams-Gibson) carried these type flags. There are two known Hardee Flags from the Louisiana Brigade today: 13th Louisiana at the Chicago Historical Society and the 5th Co. Washington Artillery at Confederate Memorial Hall in New Orleans.

If you visit the Univ. of Western Kentucky's website they actually have the 16th & 25th La's 2nd National flag displayed on the web page.