Under the 5th Amendment property could not be legally siezed without just compensation, even in War. Yes, I know this is strange to us today, but sometimes they did actually follow the Constitution.

Cotton was considered to be a war material and when it could be it was siezed and transported to markets. It was sold on the open market to support the Union War effort. That is the reason that the Confederates ordered it to be burned if it was in danger to be confiscated by the federals. And yes the Confederates gave reciepts also in such cases.

It was supposed to be the regulation that the Union Army would give a reciept for any property siezed no matter what the disposition was made of that property. There were many claims after the war for these reciepts. Some of which are even being paid today for those war debts. I know of one case were a family was paid for 40 acres of timber which the federals cut down to create a "killing zone" in front of a fortification.

If nobody claimed the damages before (and You have the original reciept) it may be possible for you to yet recieve payment for the value of the cotton burned.