The original influence on Fireforce was Green Beret but also Airborne Ranger so there is some Green Beret DNA in there.
In an Amiga Lore interview I asked one of the Fireforce developers, Steven Day, this question:
"Q: Was Green Beret an influence on Fireforce?"
"A: Yes, most definitely. But it became apparent quickly that the ST couldn't handle the volume of sprites required for that sort of game on top of the large screen scroll it would need like the c64 version."
I also asked this question:
"Q: Was Fireforce a sort of spiritual successor to Stormtrooper? There are some similarities in the two games, such as the general gameplay style and features like the dropping off of the protagonist from a helicopter/gunship."
"A: No, not at all. it was influenced initially by Green Beret and then later by Airborne Ranger. It would be more accurate to say that the start of Stormtrooper AND Fireforce were influenced by the massive amount of Vietnam films of the 80s."