What countries can Americans move to where they don't do criminal background checks for jobs?

There are none. If you wish to immigrate to another country they will do a background check before they accept you, to make sure you're not a criminal.

Ah keep tellin youse, ye're nay fecking coming here, Mr Trump!

majority of people who want to move out of america because they are financially having it hard here don't usually end up in a better situation in a different country.

they are just running away from their problems 

Eswatini.               

you can't just move, most countries won't just allow you to immigrate..unless you have a specific job skill that country needs.