Are there regulations about positioning a smoke detector in the vicinity of an air register? I would like to position it within 3 ft aerial distance but I'm concerned the air flow might be blowing smoke away from the detector therefore causing a false negative, which is like not having a detector.
You are correct to be concerned!
NFPA 72 (my cite is from the 2010 edition, but this rule hasn't changed in the last decade I reckon) 22.214.171.124 point 6 covers your situation:
(6) Smoke alarms and smoke detectors shall not be installed within a 36 in. (910 mm) horizontal path from the supply registers of a forced air heating or cooling system and shall be installed outside of the direct airflow from those registers.
So, either the smoke detector or the air register has to move, lest airflow from the register create what you describe with a false-negative result due to smoke being blown away from the detector.