The cause foe the signals to increase in speed is a change in resistance. So there is either a loose connection at the bulb, wiring at the bulb or in the column. Poor connection or short. Do any stop blinking when the wheel is turned? I assume you don't need to be moving to see this.
I agree with JPNinPA thoughts. If you concur with his last statement it would tend to isolate the issue to the column area by eliminating the lateral forces at work when driving and turning.
Try this first. Push your hazard light button a number of times then see if the issue persists. If it continues pull the covers off of the steering wheel and do a wiggle test of the wires to see if it's the wires or the switch.