Should I put a vapor barrier under a metal roof that has livestock in the pole barn building? If so could you help we with a product names?

I don't know what purpose it would serve in such an open space. What are you trying to accomplish? A vapor barrier is usually installed to reduce water migration between porous surfaces, walls and floors and between heated and non heated spaces.

I assume you are trying to stop condensation from forming on the under side of the metal roof. If this is the case, then yes. Simple 15# felt will work for you, available at any home improvement store, Home Depot etc