...income tax? is there any irs document talk about that? Also, does the credit card company need to submit the tax information about they give out the money to the reward member?

It's a reduction of a non-deductible expense so it isn't classified as income on a personal return.

If the credit card is used by a business, any reward program funds must first be used to reduce the interest expense claimed so that effectively makes it taxable as if it was income.

No, it isn't taxable income, it's basically just a return in another form of what you paid.