How to get fuel injector unstuck

I'm sorry, what is making you think a "fuel injector" needs to be "unstuck"? There are many possible causes to a rough running engine with a check engine light flashing. Most often it is related to ignition issues, such as with faulty ignition components, wires, coils, plugs, etc. A proper test must be done to see what is causing the light to flash and engine to run rough.