The easy way to do this would be to have it be an add-on feature for something like Wells Fargo Teen Checking.[1] That gets teens a debit card. The only allowed operation would be a transfer from the parent's account to the teen's account. It's not a standalone startup then, though, so you don't make tons of money. But Wells Fargo is having trouble in the mobile space, so credible app developers might find it worthwhile to talk to them.

[1] https://www.wellsfargo.com/checking/teen/