Regardless of how many cyclists use them, blinking front lights are generally not legal lighting for night riding in any of the 50 states. A steady white beam visible at 500 feet is the usual statutory standard for a front bicycle light. On the other hand, the Arizona code quoted below is sufficiently ambiguous that a blinking white light might actually comply with the code, if visible from 500 feet.

ARS 28-817 Bicycle equipment

A. A bicycle that is used at nighttime shall have a lamp on the front that emits a white light visible from a distance of at least five hundred feet to the front and a red reflector on the rear of a type that is approved by the department and that is visible from all distances from fifty feet to three hundred feet to the rear when the reflector is directly in front of lawful upper beams of head lamps on a motor vehicle. A bicycle may have a lamp that emits a red light visible from a distance of five hundred feet to the rear in addition to the red reflector.

http://www.azleg.state.az.us/ars/28/00817.htm
http://www.ci.oro-valley.az.us/dpw/B...cle%20Laws.htm
http://www.azgohs.state.az.us/bike_safety.html