If you have not already purchased the tube, talk to a steel supplier and tell them what you want. You can purchase steel tube that does not have the flash on the inside. An example of this kind of tubing is hitch receiver tubing. Here is a website that discusses flash removal on mechanical tubing:
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Going to ERW pipe or tube does not solve the problem. It also has a seam. You would have to use DOM Tubing. I think you would find this material very costly.
Personally, since the 6x6 is only going to be 36" long, I think you could grind the seam with a 4-1/2" angle grinder with the side handle removed. You only need to grind in 18" from each end. It would be easier, although more dangerous, if you removed the wheel guard. The grinder could the be held flatter in respect to the work. A safer alternative is to get a second guard and trim it back to where it is flush with the grinding wheel. I have done this to my angle grinder for use with sanding disks. I think this approach would be easier than welding up a tube from plate.
Good Luck