My fountain pen cleaning routines have changed a lot over the years, from not doing it, to doing it every other time, to every time to my current setup of: it depends.
I usually clean the pens I use a lot every 3-4 times I fill them, and that works well most of the time. And I clean the pens I don’t use as much every time I fill them. Plus that I clean any pen that are acting up as soon as possible.
Plus I always do a cleaning when changing inks. Like any sane person should.
The routine is fairly simple, I just flush the nib and feed until the water is clear, and for the pens where I don’t use a converter I also fill the body with water and let it sit for a while, while occasionally turning it to the other direction. Just to clear out any remaining ink inside there.
Then I dry out the nib and feeds with a paper towel, before refilling them or putting them away if I don’t want to have them in rotation any more.