Store an effect?

Is it possible to store an effect in the ESP8266 so that the next time the ESP is powered ON it plays this effect ?

That’s what Presets are for.
Set your LEDs to the colour(s) and effect(s) you want to see.
Click on the “+” in the lower right that says “Preset” to add a new Preset.
Change the name if you like and click “Save”, note the number it creates.

You can put that number into Config->Led Preferences->Default->“Apply preset ____ at boot”

Lookup more details in the KB: Presets