The best method is to remove the flue pipe completely, and wipe/wash the inside of the pipe and the stove with a solution of baking soda and water. Vacuum out the fly ash first of course.
The baking soda solution [one box in a 2-gallon bucket of water] helps to neutralize the acids in the ash. Normal summertime humidity will activate the acid in the ash, and you will have your flue pipes rust away just sitting there..
So: a good vacuum, and a wash/wipe with the soda solution, and if you want some form of rust preventative. or keep a light bulb burning in the stove to keep it slightly warm, to drive off the humidity.