From the context of the first post, I'm surmising PA - "Pressure Altitude" and DA - "Density Altitude"
At higher DAs or flexed, in boith cases you'll get a lower thrust/weight - either because there isn't any more to give (DA) or you choose not to use it all (flex).
Assume now that your aircraft is V2 limited (stall speed or Vmca, it doesn't matter for this). Therefore the V2 will be the same whatever conditions prevail.
Vr must be chosen such that the aircraft can achieved V2 at 35ft. This is dependent upon the pitch attitude you need to get to and the acceleration of the aircraft, because if you're accelerating at 3kt/sec and take 4 secs to rotate and get to 35ft, that's a 12kt margin right away between Vr and V2. This margin - the 'speed spread' - is obviously quite dependent on thrust/weight ratio.
Considering the flex and non flex cases, if 'un-flexed' I am accelerating at 3kt/sec I need my 12kt Vr-V2 margin. If by flexing I drop down to 2.5kt/sec accel then I only need 4*2.5=10kt margin. So now Vr is set 10kts below V2, rather than 12kts. Hence Vr is higher when flex is used.
edit: getting it all straight 