I'm sorry. No they don't. All state taxes (income, goods) go to the states in which they are collected. Nothing flow out to other states.They are also rich and subsidize the less successful states.
I live in a state that does not have an income tax or tax on groceries and a middle of the road tax on goods. Oh and my state is also a right-to-work state so it is not over run by unions. Economically we are doing way better then unionized states.