On Dewey's website, they say buy a .20 Nylon Coated Rod for cz .22's, b/c of cz's tight barrels. Do you need to buy .20 brushes and bore mops too? Or are they just talking about the Rod? Anyone know for sure?
IF you buy a Dewey rod, you just need the 20 caliber rod for the CZ; the jag and brush is the typical 22cal. That's because the CZ 22 rimfires have 0.211" bores.
https://cz-usa.com/support/faq/
However, like Dewey says, you do need the add on 17A adapter to use the typical 8/32 threaded brushes and jags.
https://deweyrods.com/product/20-caliber-nylon-coated-rod-25-inches/ (for instance, since there are several lengths)
With the Dewey 20 cal rod and adapter, a typical 22cal brush can be used. Just remember that your "22cal" brush is going to deform end up smaller. If you then use it on other 22LR's, it will have additional clearance. It is best to have a dedicated brush for just your CZ 22LR because it will end up 21 caliber after a few cleanings.
Now, to the question of how often a person should clean a 22LR rimfire. This question is perennial. I used to be someone who dutifully "cleaned it every time". However, a lubed soft lead projectile, even if it is copper washed is not going to copper foul easily as even copper plated bullets are lubed. This is just an opinion. If you have a high end, precision machined barrel, fouling will distort the imprint on the bullet since the rifling is perfect. In this example, dutiful cleaning maintains perfection. However, most sporter barrels have faults of some kind and lube and fouling can coat and fill in those imperfections. CZ barrels are good, but not perfect by any means and they do have imperfections where a seasoned barrel will typically outshoot a recently cleaned barrel IMHO.
Having said that,
there is no way that I would clean my CZ 22LR barrel after every trip to the range. It typically takes about 30 shots just to season the bore get the accuracy to return after cleaning. There is a time to clean when accuracy suffers, but no one can give a round count for anyone's particular rifle because it depends on the ammo also. I can run about 400 rounds of different RWS flavors before I can see an accuracy difference that is not elemental conditions or my shooting. If a person runs bulk ammo, that ammo is so inconsistent that a person may be able to shoot several bricks (or cases) before they see an accuracy difference.
For the 17HMR rimfire, remember that these are the same jacketed .172" bullets that are also used in 17 caliber centerfire rifles. I would clean a 17hmr like you would clean a centerfire. It is harder to tell with the 17's when to clean since fouling isn't the only thing in play that makes accuracy bad. You have to determine whether it is fouling, a bad wind day, barrel heat, or your ammo when the accuracy suffers. While some boxes are better than others, most 17HMR ammo has an ES of 200fps+ for every box of 50 (the difference between the slowest and fastest shot).