Me too, just pull back and it seems to stop without flipping.

No, it doesn't work like that with Aviator flight stick. Because there are no manually controlled brakes with Aviator, the AI will make a fatal auto-brake at exactly 57 km/h which will flip Spitfire inevitably. pulling back works with the xb360 controller where you can lean on the right pad for brakes. It doesn't even matter there what you do with the left pad.

Works for me with an AV8R. Firing the guns while on the ground works as a slow break as well.

With the AV8R a usually stop by using the rudder violently left and right as soon as all wheels are firmly in the ground...have to try out with guns

Are you sure you are flying Spitfire on Sim, all other planes flip at 57 but not enough to roll over. Flipping happens only on Sim/Spitfire/AV8R. Nothing will result in controlled recovery of the 57 flip. It seems to be purely random when the flipping is violent enough to nose down Spitfire, but it will always happen in at least 9/10 of the cases. I have already suspected 10 different reasons how to prevent this but none of them really works except randomly.

I just tried the firing, but it still flips at 57. It doesn't even help if I drive the runway in circles a few times. Whenever you slow below 57, it will flip.
There is still no cure for this.

Weird AI behaviour
 

I've also noted that your plane will sometimes take off by itself and the flight controls freeze until you are some way from the airfield.

Anybody else experience this? Any reasons?