Ideally you need the patches for that particular jag. I like Dewey stuff and try to use their patches with tipped jags. You almost never find a full stock of Dewey stuff from any one vendor, they make so much different stuff I guess. It seems like everytime I see the stuff for sale there's a new piece I never saw before. Only one I know of that makes a high quality dedicated M2HB rod and their 7.62 AR chamber brushes and mops are pretty nice also.
I use their Parker Hale jags more and more, and if you use 'em right, wrapping the patch cornerwise around the jag, they work really, really well. Which is great because I have a lifetime supply of army 7.62 flannel patches and they work great with these, better than with thin patches.
Then I take the small Dewey adapter and I JB Weld a piece of nylon coated steel cable stripped back a bit on one end, and use the patch loops on these for pull throughs (I forget the size but there's only one size that has the same OD around the nylon as the adapter and that'll fit a .22 barrel just right). It's a cheap way of making a high quality DIY Otis type cleaning kit for pretty much all calibers. I use flannel with these too. and just cut to fit.