Best way to handle flipbook animation on mobile devices?

Hey! I’m making 2D side-scroller game. I sometimes need to play cycle animation by Input Touch event, so it would be called only once and then I need to play run animation til the finger is released, for example. Also I sometimes need to play animation for one time, for example, attack animation by pressing widget button. I’ve solved this problem by handling animation on Event Tick but I think it’s complicated solution and may cause troubles. Also it doesn’t handle animation properly on multiplayer because of server-client data transfer delay I suppose. Is there any way to handle animation with special functions (not using Event Tick)?
Any help or advice would be apreciated!
P.S. it’s single player game; at first, I tried to make it multiplayer but I faced problem with flipbook replication, here’s my question: Replicating characters' variables problem - Asset Creation - Epic Developer Community Forums