You can get a hand pump at advance or auto zone. Even wally world would have them.

The pump I use is a cheapo external fuel pump that my dad had laying around for years, I just used some jumper leads to connect it to an extra battery laying around. I found a scrap hose that would shove inside one of the ports on the side of the cooler and ran it for around 30 mins.

I believe I removed the thermostat from the cooler too, this may be something you want to look into. I cant remember for sure since this was years ago.

While flushing... tap the end caps lightly with a rubber or plastic mallet.
Flush both directions.
You can also do an ultrasonic cleaning by laying a out-of-balance die grinder on the tanks while flushing.
Finally x-ray the tank.
Barry