The advantage of a DL AmEx Platinum or Reserve card is that it give you status miles based on spend thresholds as well as redeemable miles. You can get Silver status with DL (or almost get there) just on your kid's college expenses. AFAIK they will give him an authorized user card in his own name if you want this.

Note that many colleges impose a fee (several percent) for paying with a credit card, similar to the fees for paying most taxes with credit cards. This can exceed the value of the miles or points earned on the card.