yes, you can book a flight for whomever you want if you have a regular avios account.
If you have a household account (ie you and others in your house linked together) then things are different.
I have done it many times and you don't have to fly with them, be there at check-in etc etc, you are effectively acting as a travel agent for them.
NB. It is against the rules to "trade" your miles ie: You are not allowed to buy a flight for someone else (on miles) and receive recompense for doing it