You do not need to take it back out. It is difficult to prime and that is one of the obstacles. The second obstacle is a bend in the tubing near the front of the system. Both can be addressed by opening the system just after the pump by taking off the outflow AN fitting from the pump. You will need to make a new hose with the same type of AN fitting to connect a pressure pot to the pump, and pump new brake fluid forward, directly into and through the pump, and forward filling the brake fluid reservoir and out the reservoir overflow. You will have a clear tube attached to the outflow so you can see when there are no more air bubbles. When that is accomplished, take off the hose from the pump and re-attach the posterior part of the system to the flap pump. Do this quickly so as not to introduce air. Then move your pressure pot to the rear of the system and attach the pressure pot there. Push clean brake fluid from the back to the front until the fluid exiting the reservoir overflow tube is without air bubbles and is clean. Disconnect the pressure pot and seal the system.
As I recall, the gear release handle needs to be in the down position to push fluid through the pump (but I may be wrong on this). There are only 2 positions so just try it.
Once the pump is primed, the flaps should work directly. You may need to work the flaps and top off the reservoir. It is 4 to 4 1/2 pumps to lock-out. Time retraction per the manual. The adjustment screw is very sensitive. 10-11 seconds to full retraction is about right.
Dont try to be cheap on this one. Buy a good pressure pot (BRAKE BLEEDER TANK - Aircraft Tool Co.- aircraft-tool.com) and a smaller pressure pot to fill the reservoir from the front. Most importantly, make up hoses with the proper AN fittings to connect to the hydraulic pump, the rear of the system, and to reservoir - (Vaper 19419 Red Spot Spray Non-Aerosol Sprayer (Red) - 32 oz - Amazon). You will need to find fittings to connect AN Fittings to the can. This will make life much easier, the project go faster, and will eliminate the mess usually made from leaking brake fluid everywhere. You may want to install pressure gauges on each.