I am planning to replace my Oil Cooler and EGR Cooler. If the EGR cooler is already leaking, is it okay to perform a coolant flush?

 

As long as it's not flooding your cylinders or running coolant out the tailpipe it's fine.

 

That could be a dangerous move if you should hydro-lock. Myself, I would remove the lower hose, open all pet***** and get what I could out of it without running it just using a garden hose to flush it. The t-stat would also have to be removed. The safest precaution when done would be to remove the glow plugs when you first turn the motor over. A lot of extra work but better than a trashed motor. You could also just flush it after the cooler work but you then take the chance of plugging the new oil cooler.