There are commercially available chips but... you need to be a volume customer to get at them. My suggestion to you would be to go get the cheapest possible HP inkjet printer, the cheaper printers have simplier control systems. Then probe the lines that go to the black and white cartridge with a scope.
The internal resistive elements are driven by firing pulses from an IC on the mother board. Usually around 24-36V but it varies. These short pulses heat the element and spew ink out the nozzle. There's a matrix for the simple cartridges that lets you select each element.
It's simple enough that even in the lab you can use a power supply to put a short pulse on a firing line and the cartridge will spit ink for you. The length of the firing pulse is important, too short no ink, too long way too much ink, way too long burned out element.
Behind the chips that drive the head is a controller, it's job is to take the print data, be it an image or the image data sent down from the print data and convert it to low voltage versions of the firing pulses. Of course there's image processing magic in there too but if you're just doing a stamp you don't have to worry about that. Anyway the controller comes up with the firing pulses that are then fed to the high voltage pulse creating circuitry (a custom IC in the printers case). Here's one that can be found at digikey albeit out of stock...
So that's kind of what you'll need to come up with. A method to convert your picture or drawing into firing pulses, and some circuitry that will convert those low voltage pulses into higher voltage pulses to drive the heads.
I should also mention that there's more to inkjets than just printing, maintenance is an important part of keeping the head from drying up. That's that strange thing your printer does whenever you turn it on or before it prints. Usually this involves spewing ink out of itself into a pad at the bottom of your printer, then having a wiper arm wipe itself off.
You won't find any datasheets on inkjet heads, it's all under NDA, even then they won't tell you anything too useful and you have to reverse engineer a lot of things. So that's what you're in for, I've reverse engineered many inkjet systems and wedged my own electronics in there to control things so it can be done.
If you're a company and not just a guy working on this, there are programs for low volume custom inkjet based products but you need to have $$$ or connections to find your way in.
I've always thought inkjet printers are more complicated than most people think :)
