You don't need to pay for the tickets with the delta amex to get the free bags, the amex just has to be linked with your skymiles account. Your skymiles account is yours and yours only, though, it can't be used for anybody else. Everybody has to be booked together for them to get free bags.
If you're all booked seperately but are on the same flights, the ticketing agent might waive their baggage fees, but ymmv