No, you can't claim miles for someone else's flight.

If your friend doesn't want to use them, in addition to gifting/transferring them he could also convert them into Hilton Honors or IHG reward points. I think Marriott was also an option but they're not currently listed on the Flying Club site as a conversion partner.

If none of those options suit he could create a Delta (or other VS partner) account and earn miles in that program.