There is specialized equipment that is used to clean injectors, most of which are the solenoid types for EFI systems. The machines have various adapters to mount different injector designs, and I'm sure some can handle the KE type mechanical injectors. Enough system pressure is required to open the check valve.
Combined with an ultrasonic wave generatior, a strong cleaning solvent is run through the injectors and the flow rate is also measured, so once they are clean you can determine if the flow rates are in spec and also visually inspect the spray pattern. Any that are out of spec should be replaced.
Any deposit buildup in the injector or the check valve seat will affect flow rate, and any deposit buildup on the injector skirt can affect spray pattern. Either of these can cause idle stability problems.
Some shops may have their own cleaners and some sent them to outside vendors. You'll have to check around locally to find a shop or vendor that has a machine that can handle the KE injectors. In the meantime, the following link to GB Remanufacturing has some information on injector cleaners. They sell them to service shops, but I'm not sure if their product line will handle the KE injectors.