My friend has applied for a UK Family Visa which has been rejected. Can he claim a refund of the application fee?
No, there are no refunds of visa application fees. This is true in the UK and many other places as well.
In the UK the only times you may get fees back are if you voluntarily withdraw your application before it is processed, or if you are reapplying whilst concurrently appealing a prior rejection (in which case you may receive a refund of the second application fee but only if the appeal is successful).