How do I tell if my 340 is internally balanced?

Will it hurt to put that flex plate on it if it is balanced.

Yes, if it was balanced it would throw the balance off. Mallory Metal is very noticeable. Horizontal holes in the crank. I would be surprised if it was internally balanced. Not much now to take the crank, a piston, pin, ring set, rod, and rod bearing in and have it checked.