This option was moved to Accessibility from Features some time ago. If you don't have it in either menu, then you are likely the subject of the 'test' King sometimes run, which removes features from certain groups of players.
Oh my goodness, @MannyFae I am so grateful for that post! Since when is this change? As soon as I saw that I went into Accessibility and turned off the flashing effects!!! What an improvement! Why did no one tell me I could do this before?
I believe it's been around three months. It's surprising that there was no announcement despite the fact that turning off flashing effects is helpful to many people.