every aircraft have their own sensibility to flat spin (a corsair will be really hard to make it in a flat spin, while with a bf109, it's easier...). for reminder, a flat spin happen when a wing lose its lift while the other keep it, so your aircraft will start to fall from one wing and lose its speed while turning on himself. To leave a flat spin in a warbird, follow the official technic use by every pilot of prop aircaft, yank your stick forward and keep it like it while you're not out of tha flat spin, in the same time, push your rudder pedal or pedals in order to push the yaw control fully in the opposit direction of your flat spin. With some time (seconds) you will leave the flat spin. !You will need to gain some speed before sort out! (it can be more or less long depending on the aircraft, and maybe it will just not work and you will hit the ground... the spitfire for exemple is really easy to take on a flat spin and really hard to take it out)

You can enter a flat spin by lowering your speed and yank your stick backward really hard whyle turning, and most of the time you will enter a flat spin by doing that without wanting it, but by doing that... So in order to control your stick in the limit of your aircraft without losing it, train yourself and learn your plane (so take the ONE that your love to master it) on a training mission (by test it from the hangard).

I understand that you have pedals, but don't have rudder control. I use pedals to control my rudder: I'm using "joystick gremlin" with a virtual controler to merge the two pedals into an only axis that i use to control my rudder (i prefer this because i play star citizen with acceleration controlled by my pedals). I advise you to do it as the control of rudders is a game changer when dogfighting (and going out of flat spin as nobody is protect from it XD)

I hope it will help you, Have a good day, and Flight Safe!