Not all the time, but eventually after a few minutes.
It doesn’t, for me. Refresh rate too low on your monitor?
It doesn’t for me either.
Graphics card drivers?
Are you using Chrome? There is a known issue in Chrome that can cause flickering with things like YouTube.
Go under your advanced settings. Somewhere there is a setting to enable hardware acceleration. Turn that setting off and see if that helps.
Firefox can have a similar issue. There’s no easy checkbox to enable/disable, so you have to go to your about:config to change it. Set layers.acceleration.disabled to false.
If it’s not your browser that’s borked, then video drivers (as already suggested) would be my second guess.
Addendum to what ECG said:
Before you shut off all hardware video acceleration, try turning off hardware video decoding. That way the rest of your browser is still accelerated.
On Chrome: type chrome:flags into the address bar and press enter. Then type decode into the search box on top. Then click the Enabled button under “Hardware Accelerated Decoding” and select Disabled instead.
On Firefox: Type about:config into the address bar and press enter. Then type hardware into the search box on top. Find the option “media.hardware-video-decoding.enabled” and click the toggle button (⇌) on the far right to change it “false.”
Are you guys (checking before I embarrass myslf; of course you’re all guys 
) saying my $50 Kindle Fire 7, using the garbage browser it came with because it lacks useable internal memory, lacks horsepower?
That’s too bad, if so.
But even a $200 tablet in the 7 to 8-inch screen size range can do YouTube just fine; it’s my go-to for videos. Maybe that’s the minimum spend for a YouTube viewer…?
Maybe Amazon and Google’s war has gone to the street. I’ve been expecting this since I saw how many apps are incompatible.