The use of linseed oil is to fill the pores in the rusted surface. it is not the intent to paint the barrel with the oil. It's kind like having your driveway sealcoated. The purpose is not to seal the tops of the gravel, but to seal the gaps between the rocks.
What I have done in the past is to coat the barrel with linseed and lightly wipe it after several hours. This gets rid of the surface oil. Then I take a propane torch and lick it over the barrel enough to lightly char the oil. Then rub it down with fine scotchbrite. This should not harm your rusted finish but should remove any surface oil remaining, but leaving the interstices filled.