This may be a long shot but I'll try to help.

I imagine if you put a Volt meter on your battery and rev the engine, you'll see a corresponding increase/decrease in voltage with RPM. This is not typical (not a lot of swing at least)....

My guess is that when you rev up, it blinks faster (although you did not specify)... but if that is the case, the circuit is getting more voltage and is therefore able to pass more current through the blinker relay. Most of those I believe use heat to 'bend' a contact out of the way, turning the circuit off, then as it cools it makes contact again, and so on.

I think you have a bad alternator or some other aspect of your charging system, which is causing low voltage at low RPM. As you rev the motor, voltage goes up and it blinks at the appropriate rate.

If the voltage is constant at the battery, check as close to the blinker relay as you can and verify it is constant as well (on the input side).

If you have an under drive pulley, you'll be turning the alternator slower and it can cause low voltage at low RPM.

Voltage should be around 14v +/- 1v at the battery with the car running. If idle voltage goes down to 12.5v or lower, your charging circuit is limping along at lower RPM.