workingonit,
The Kent-Moore did show up in a search. The tool is specifically made to flush oil coolers. Transmission lines bolt to it.
A 5L40E case connection looks like picture #2. Older transmissions have threaded holes. A 5L40e has o ring style connections.
Adapters are made for 6L80E and later model transmissions. -AN fittings are secure and leak proof for high pressures. With an adapter, I can install an external cooler myself. A local shop quoted ~$500 to install a cooler. All they would probably do is cut flex the hose part. At the barb, they would use clamps to hold a rated hose. One clamp is not enough. A crimp would hold. I would be hard to trust even two clamps on single barb line.
Real OEM has the part number for the lower hose as 17227509301. The other is 17227509300. For the cost of one hose, an external cooler is not much more. Other than labor time to install it behind the AUX fan. Right above the engine oil cooler.