What does “Do Uncle Sam” mean?

Solution 1:

I've got to admit I'm not 100% sure on this one, but I think Archer is using the verb to do in TheFreeDictionary's sense 12 (slang) To cheat; swindle. And Uncle Sam (US) is slang for America (the nation, government, people, military, etc.)

By stashing the money in a Swiss bank account (commonly understood to be untraceable by tax authorities), Metcalfe is cheating the American government of its rightful share (of tax which should be paid).

To get a kick out of something/doing something is another slang/informal usage meaning to enjoy doing something very much. The implication being that even though Metcalfe is a billionaire (who shouldn't actually need to chisel the government out of a bit of tax), he just likes doing it for "fun".