There's a number of factors involved, but seeing as you highlighted CONSTANT IAS.................
With all other things being equal, Drag is directly related to EAS (Equivalent Airspeed), and not IAS.
With increasing Pressure Height at a constant IAS, EAS, and therefore Drag, is reducing. Thus, for the same IAS, Fuel Flow will be lower at higher altitudes (Until Mcrit comes into play).
Regards,
Old Smokey