This would take time to transport especially as there are no scheduled flights to Kinloss.
Another issue is that would any commercial company want to loan spares to the RAF if the aircraft are not being maintained under EASA or FAA legislation - sending spares 'outside' of the EASA/FAA system could prove problematic from an ongoing paperwork trail.
At the risk of sounding like a smart ass.....there are Air Taxi Operators that could fly the part(s) to Kinloss under an "On Call" Contract.
If the RAF needs the part.....they can buy the part from the Civilian Operator just as they would buy them the usual sources if that was the last option in getting the part and putting the aircraft back into service.
It isn't rocket science.
It does require some commonsense which is a rare commodity within every government operation.