According to a post by an Amazon employee on the amazonforum, yesterday, April 5, Amazon is: aware of the problem, there is no fix yet, and be patient while they work on a fix.
As I just received my Fire HD8 a few days ago, and it updated itself yesterday, and then the screen started to flicker weirdly on occasion, I'm relieved to know that it appears the problem is caused by the recent defective software update, rather than a defect in my brand new device/hardware.
I guess they're working on a software fix and will send out another update soon. I hope.