In my opinion there's no need to flush FIP. Rather the tank and fuel (main) lines. Just bring good (clean) fuel to the pump.
Flushing the FIP with this mixture will clean only the "fuel area" inside but if you let the dirts to go out through the valves it could cause to stuck (by this dirt) certain outputs. I think that's the situation. Nothing else couldn't happen. In this pumps there are cone-type valves, so you have to "just" unscrew the output fittings (only this 3 not working), pull out the cones and flush entire dirt outside. Don't forget to apply correct torque by screwing the fittings back. If the pistons are not stuck completely (the car ran properly before), it should run good too after this operation.
When I first flushed the pump (without cranking the engine) dirty stuff came out, then clean stuff. Then I tested again with engine cranking and got cleaner out of 3 injector lines. Then I took off the tops of those injector lines that nothing came out of and felt with a long tap and could feel that the piston was not moving. I sprayed cleaner in there first and tried again, no movement. Then I used a tap to gently tap on the pistons and one immediately un-stuck. Then when I crank the engine with the tap resting on top of that piston I can see the tap moving up and down with the injection pump piston. I did the same thing to the other stuck pistons -- they took more tapping. After all of them were moving I put my test lines back on the top of the pump and cranked it again for a while (repeatedly). This time I got fluid out of all 6 pistons (see picture.).
Everything in the fuel system of this car is dirty and laquered. The tank was a mess -- the supply tube from the tank completely clogged with gunk. It is clean now. 'The fuel pump was stuck and gummy. I rebuilt it. I have flushed the forward and return lines. I removed the fuel filter and housing and cleaned everything. It had a layer of goo in it.
The car has not run in probably 15 years. Maybe only 10 years. It has been a long time. The engine cranks great and I changed the oil and it has good oil pressure when cranking. Now I am cleaning the injection lines that run from the pump to the injectors. I'm doing this by soaking the lines in evaporust, then blowing diesel through the injection line, then blowing carb cleaner through the injection line, then blowing air through the injection line.
The last two things to clean are the cold start valve (and replace the two rubber rings) and the injectors themselves. I have the Mercedessource MFI pop tester/cleaner device but I have not yet removed the injectors.