Secret Agent F-8 is an agent with American Intelligence.
That narrows things down a bit as it removed all other nations but from then on, we have no real idea. Since neither of the two recorded adventures are as yet available to me, all I have to go on are the covers of the two publications in which these missions were described, and that is almost nothing because there is no way of knowing which of the stories contained therein are represented by the illustrations on those covers.
So all we really have so far about Secret Agent F-8 is that he belongs to one of the groups mentioned on one of those illustrations: F.B.I., Secret Service, Postal Inspectors, Narcotics, Coast Guard, Customs, Naval Intelligence, and other Government Agents. That same cover mentions the title of the first adventure and lists it as a "Great Spy Novelette" so we can for the most part eliminate Postal Inspectors, Narcotics, Coast Guard, and Customs (yes, they could be connected to espionage adventures but likely not).
That leaves us with the FBI, Secret Service, Naval Intelligence (what about Army/Military Intelligence?) and "other Government Agents". F-8 could logically therefore be a G-Man, T-Man, G2-man (I made that up) or an Other. I took the safe way out and just dubbed him as working for American Intelligence, a wonderful catch-all that says a lot without giving much away.