The admins have said that an animation toggle is coming with the coli rewrite but that it won't make battles faster.
http://www1.flightrising.com/forums/ann/1329753
Scroll down to the big "Update: Coliseum" section. Or just read this:
From this menu, you can disable the following visual effects: Weather Effects (such as snow, rain, embers, bubbles, etc.) Animations (abilities, floating, dragon jumping, etc.) Elemental Flash/Screen Shakes (the effects that happen when you score an elementally-charged attack against what that element is strong against) NOTE: Disabling these effects will not alter the speed at which battles progress.
Re: What do you want to see from FR in the future?
http://www1.flightrising.com/forums/ann/1329753
Scroll down to the big "Update: Coliseum" section. Or just read this:
From this menu, you can disable the following visual effects:
Weather Effects (such as snow, rain, embers, bubbles, etc.)
Animations (abilities, floating, dragon jumping, etc.)
Elemental Flash/Screen Shakes (the effects that happen when you score an elementally-charged attack against what that element is strong against)
NOTE: Disabling these effects will not alter the speed at which battles progress.