You wont really be able to flat spin a trainer very well. They just are not made for it. But you can play with the control inputs and get a little bit of a spin out of them, as you say it is going to spin with the nose pointed downward and just will not flatten out.
Flat Spin
When you want to "flat" spin upright you use full up elevator and full rudder in the same direction, and then you only use enough aileron in the same direction
to get into the spin. Once the plane enters the spin you get off of the ailerons (as needed) to flatten it out. Throttle also plays a big roll in flat spins. Too much throttle and you will pull the nose up too high and can even flip the plane over backwards, not enough and you cant get it to really flatten out and the nose will ride pointing downward a little through the spin. It also helps to be a little tailheavy to get a really good flat spin.
For an inverted flat spin you input full down elevator and the rudder and aileron inputs are opposite. ie. left rudder and right aileron or vice versa. Same rules about centering the ailerons and adjusting the throttle to flatten out the spin apply.
Normal Spin
Normal spins are basically the same inputs as flat spins, but you dont use any throttle, you spin at idle. The planes spins with the nose pointing downward somewhat. Depending on the CG and control throws the amount the nose points down will vary.
The perfect spins (we are talking RC here all of you aerodynamic experts) will descend vertically at the CG of the plane, as if the cg were affixed to a line on a plumb bob (with the exception of wind drift) and the nose and tail will rotate conically around the CG. The plane sortof looks like it is "sitting" as it spins. It should not barrel roll and it definitely should not aileron roll.
Ideally you enter a spin by stalling the airplane. You get up real high and chop the throttle. The plane will slow down to a stop and stall either by falling forward or by dropping a wingtip and falling forward at the nose at the same time. Most folks start to discretely feed in up elevator as the plane comes to a stop which will stall the plane more visibly and cause the nose and one wingtip to drop more dramatically. But thats cheating.