I think you would be better with a wider, less tall option, but I could see this being done by a skilled TIG welder. I'm afraid silver solder would be difficult to do and would probably not hold up well unless the boiler were completely stationery.
Solder likes to run. You can't just "Place it" like weld. It just tends to flow. If you made a piece to go between the kegs to support and hold the solder, then it might be possible. For the cost of used kegs and the work I think it would be easier to find a large used kettle somewhere. I know I've seen 20 gallon pots before.
OR, you could find a good, clean Stainless Barrel and convert it. In that case it would only require cutting and maybe welding a handle or two on it.