Please, please do not use the flash mode. The idea is that you get more attention and that works, yes. But it is dangerous for people around you and yourself. A brilliant blinking light is a hazard to look at. It is a heavy distraction for other cyclists and drivers. Their eyes can not adjust to it.
The other reason is the calculation of the distance. With a flashing rear light you can not recognize how far it is away. Try it. You can not recognize if the distance is increasing or decreasing. Here is just not enough time see if it gets brighter/bigger.
I use the B+M Toplight Line. This is a rear light with an integrated reflector. Like the original Strida rear light, it fits on the carrier. It uses a standard AA battery. The front light is an B+M Ixon IQ, which contains four standard AA batteries. The front light has two modes - 40 lux and 10 lux. 10 lux is enough to ride in a completely dark park. None of the lights has a flash mode.