You don't need the anti flicker device. The DRLs on our cars are independent of the main headlights. If the headlights doubled as DRLs, then yes, the anti flicker device would be needed.
With regards to the HIDs cutting out when the headlights are set to auto on engine start up, I haven't noticed them cutting out. I've had mine installed since January. I'll pay closer attention the next time I start the car up at night. But I think I would have noticed something by now. But this can also be due to the additional relay harness I installed which came with my Xenon Depot kit. The relays are inserted between the stock headlight harness and HID ballast and wired into the battery.
2019 Toyota C-HR LE Silver Knockout Metallic
2013 BMW 135i Carbon Black
2009 Ducati 848 Pearl White/Black
2004 Kawasaki Ninja ZX-10R Black