Odd one...
What kind of oil exactly did it seem like? motor oil? cooking oil? or just a black ooze?
There is no reason oil should be in a propane tank. If there is oil then I can't see how it would matter. The propane comes out of the tank as a gas, and if there is oil in that tank it should not vaporize and come out with the propane gas.
Oil in the copper tubing on the camper carrying the propane should not matter either. It should settle out or just stick to the walls and never make it to the appliances.
If oil somehow made it to the burners then what would it do? burn?
I suspect your oil could be a deteriorting rubber hose.
As for the question, how to flush a tank... It will be cheaper to just get a new tank. I assume you have a 30 lb tank, not an exchangeable 20 lb bbq tank.
You cannot flush it. A qualified propane tank business will be able to remove the nozzle and then have full access to the inside of the tank, or maybe they have an easier method.
Flushing your plumbing system? No need that I am aware of unless it is full oil quarts of oil, and if that is the case you have some serious problems that cannot be solved with advice.