Do it all at once. You goal is the FLUSH out the bad shit, not to just get it wet.
Use tap water. The CaCO3 dissolved in most tap water will help neutralize acids. Adjust the pH of your flush solution to 7.5. Check runoff after the first couple gallons.
The final flush should be with a solution of 1/4 strength complete fert at pH 6.8-7.0 (since you are starting low and a slight drop will continue).
I'm guessing you're in a peat-based medium and have been in the same pot for at least 8 weeks?