Is he booking a whole airplane? That's what it sounds like in Romanian. The way we Romanians would say it:
El își ia un bilet de avion / la zborul X.
El își face rezervare pentru zborul X.
El rezervă un loc în avion.
The way the English is also sounds like he is booking the whole plane - perhaps he is organising an evacuation? We would say he books a flight or books a seat or seats or buys a plane ticket or tickets or something if he is just booking one person or group's flight(s).