I have spent some time finding out how to animate tiles in a tile map loaded from a Tiled map exported to JSON. At first I built a utility class called TileMapAnimator (TMA) to animate some tiles using manual data and eventually I extended the class so that it could load animated tile data directly from the map files. With TMA you define your animations in Tiled and load them directly into your Phaser game!
I'm sharing this code in the hope that others may find it useful. If you have invested into loading Tiled maps using the built in functions, I believe you can include animations in you