Thanks a lot for the information on the flags- I didn't know about them. Using google I did some looking around and found a webpage that shows the Confederate flags held by the state of Iowa with the link below.
I noticed you mentioned that two flags were captured by the 33rd Iowa and are in the collection. The site shows one flag of the 37th Arkansas. It shows another at the top left that is called "Bell Everett." Because of the name Bell, I thought it might be the other flag...but I have no idea what the Everett would be referring to. I also noticed that the flag on the middle of the left side is very similar to the flags of the 15th NW Arkansas Infantry and the 17th Arkansas Infantry. It is reported to have been captured at Corinth. I can't help thinking that this is a flag from an Arkansas regiment.
Many thanks again for the lead on the flags, as I had never seen the Iowa website before.