Your child is already a British Citizen by descent from the moment he was born and you can directly apply for a passport for him.
I don't think you need to register his birth abroad to obtain a passport, just apply for the passport via post and send the Spanish birth certificate along with a certified translation into English. (And obviously his dad's documents as well)
I am not sure which advantages registering his birth abroad may have, some other members may be able to give you some more input regarding this

All information given is just my opinion as a member of this forum and does not constitute immigration advice.