F-4 is an agent with Air Intelligence.
When we first meet this intrepid warrior, we are told he is a "Fifth Column Fighter". We are also informed that he is a "spy hunter". From both of those and the missions he gets sent on, he definitely is involved in counter-espionage as his job is to hunt and fight those seeking to steal or destroy from the country. We also learn right away that his area of expertise is aviation and whether it is flying a one-man pursuit plane or piloting a bomber or operating the machine-guns on any number of craft, he shows over and over that he knows a thing or three about being in the air.
He also knows more than most about crashing to the ground because so many of those in the skies along with him do not want him there and can prove it. He is both an excellent crash-lander and a lucky son-of-a-gun because several of the collisions should have killed him several times over.
The first few missions we have recorded make it difficult to be certain what his nationality is. He is operating in Europe and answering to British officers so it would not be illogical to think he was British. Halfway through the 15 missions we know of, however, it is clearly stated that F-4 is American and as the U.S. grew closer to joining the conflict with Germany and Axis agents start in earnest to stop American aid to the Allies, he leaves the European theater and heads home.
There is virtually nothing we know about F-4 the man. We do not even learn his name is Rex Keene until near the end of the tales. We do not know where he is from or how he got his start as a secret agent. Conjecture is all we have.
We surmise he is in his early 30s based on his appearance and his demeanor. He is in great shape with rapid reflexes shown in his flying skills. He is a good fighter with fists and guns. He has to have a very hard head because he gets bumped on it nearly every mission. And he is fond of hats.