Can you apply for an American visa with the intention of going to the UK via America?

You don't mention where you're travelling from, but if you're an international traveler seeking to travel to or transit through the U.S. under the Visa Waiver Program then you will need to apply for an ESTA before you travel. If you're traveling through the U.S. and you're from a country not covered under the Visa Waiver Program then you will need a Visa. If you have a visa you don't need to apply for an ESTA. Unless revoked, an ESTA is valid for 2 years from the date of authorisation or until your passport expires, whichever comes first.