Printer companies specifically avoid doing this because their margin only comes from ink sales. They usually lose money on the printer itself. This is true of most accessory-based consumer electronics; Microsoft loses money on every X-Box line of product sold, and makes a killing on licensing developers to make its games and online marketplace surcharges. When I worked retail, a Lexmark rep once revealed to me that we were buying cartridges for $20 that we were selling for $45 and that Lexmark only spent $1 per cartridge to manufacture and ship them, but that they averaged a $10 loss per printer they sold, and that loss carried forward. That's why the guy at the store just shoves ink in your cart without asking, and why the printer ships with half-filled ink and calls it a "starter" half the time.
This means you have more to deal with than just cleaning the cartridge. You need to know your cartridges a little.
- Don't do this with an HP inkjet. They integrate the printhead onto the cartridge, which is sort of nice, but they also sometimes rig them to detect inks of a different density and refuse to print. I don't have a link for that one, but I've seen it happen. If the ink is thinner, it may fail to detect, but the custom head may just vomit ink all over the page because it's expecting a certain density. Even just normal ink refills with them takes a little care, and ink quality matters.
- Lexmark will work, but not all of their cartridges are refillable.
- Single-color cartridge printers (i.e. C, M, Y, K are in their own containers) are ideal. Brother, some Canon, Xerox, and Epson all do this. They warn that using your own ink voids your warranty, but the cartridge will accept the ink. Also, many of the cartridges are clear, so you can visibly see the fill level, and you don't have to worry about screwing up filling a tri-color cartridge.
Knowing the above, I'd advise starting with Item 3 on the list; get a printer that uses single-tone, individual carts. Got one? Great. Clear cartridge? Even better. Now to prep the cartridge.
You don't want to soak the cartridge in bleach or vinegar. Bleach is a bad idea anyway as it leaves a residue which may affect the ink. Vinegar will break the dried ink up and flush it out, but it's likely to damage the rubber seals on the cartridge or expand the rubber so that it doesn't fit right anymore. Always start with hot water and just observe the cartridge contents to see if it flushes (clear cartridge benefit, of course). If you get all of the ink out, great. If you have splatted hunks of dried ink inside, then vinegar might be your only (safe) solution, but don't let it stand for long, or you can damage the cartridge as mentioned above.
Allow to dry before refilling with your ink. Keep in mind that a viscous ink and a watery ink aren't the same thing; if your printer normally dumps thin ink and you put in conductive ink, it may give you some spotty or splotchy results. I'd start small, here.