Can I use a Flex Spending Account to pay for my child who attends my wife's in-home daycare?

My wife started an in-home day care business, and our child, is one of the four children who attends. I was wondering if her business can bill me and I use my Flex Spending account to pay for the tuition. This way, I could avoid paying income taxes on that money used through the FS account. She then, through normal business write-offs, could lower the income tax she would have to pay and ultimately save us some money. Is this legal? We are both very new to running a business so any advice on this would be greatly appreciated.

Thanks in advance!

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