It can depend on your local laws however if there is a sign posted no turn on red then you cannot turn left on the red light even if it's blinking.
The blinking red light means to stop and if there's no sign stating no left or no right turns then you can turn left or right on the blinking red light as long as it's not a red arrow blinking.
Never turn left or right when a light has a red arrow blinking or just a plain red arrow.
You must not proceed to turn until that red arrow turns green.