They don't usually do any tests to be honest and just diagnose on symptoms. Hammies have so little blood you can't get a test and there are few antibiotics that you can use with hams that they normally just treat straight away rather than expensive cultures so you will most likely get Baytril.
Chronic kidney failure is quite slow progressing and a reduced protein diet can help this. They normally appear quite fine with it. They only get really poorly in the end stages and can cope with quite reduced function for a good long while usually. Almost a normal life span
There is no treatment as such for kidney failure so it is best to not fret and enjoy the time while they are comfy and happy.
Let us know how he gets on.