Does airspeed impact fuel flow?
I don’t believe that airspeed directly affects fuel flow, but it may impact other variables that can have an influence.
I don’t have a flight manual for an F-104, but for the EA-6B the manual says the following about the fuel control unit on the J52P-408A engine: (straight turbo jet, non-after burning, 1970s technology)

“The engine fuel control is divided into a computing and metering
section.  The computing section monitors throttle position, burner
pressure, engine speed, and compressor inlet temperature.  These data
are translated into a fuel demand that is relayed to the metering
section, which measure the correct amount of fuel from the engine fuel
pump the fuel pressurizing and dump valve.”

Of those four inputs the primary would be throttle position, with metering occurring to dampen out pilot inputs and ensure smooth operation.  The other three may be influenced by environmental conditions such as airspeed, altitude, etc. but airspeed itself is not an input.
Modern FADEC, (Full Authority Digital Engine Control) engines might be different.