Learn English – a “cike” as in “taking the cike”

The Phrase Finder has "Don't try to teach your Grandma to suck eggs" is older than you might think, but without any explanation of the egg sucking part.

Meaning

Don't offer advice to someone who has more experience than oneself.

Origin

These days this proverbial saying has little impact as few people have any direct experience of sucking eggs - grandmothers included. It is quite an old phrase and is included in John Stevens' translation of Quevedo's Comical Works, 1707:

"You would have me teach my Grandame to suck Eggs."

A little more on the egg-sucking part from Wordwizard:

Perhaps its meaning is getting lost in time as few people nowadays literally suck eggs. Many years ago people would suck out the egg contents by piercing the egg at both ends and then sucking on one of the ends. You could reverse the procedure and blow out the contents also. It was such a commonplace procedure then that to "teach your grandmother to suck eggs" was like a child trying to teach as new something the grandmother well knew how to do. The saying still survives despite the fine art dying out in our "civilized" and salmonella fearing culture.

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".