How much tolerance is acceptable on the chainline of a fixed gear conversion?
There is no hard and fast limit. The farther off the cogs are, the worse vibration and wear you will get. My personal experience is that a couple of millimeters off is still smooth and at 5 mm the chain will be noisy but still work. 

On a singlespeed it's virtually impossible to throw a properly tensioned chain without breaking cog teeth, but bad enough chainline will wear them out and make that easier.