With TileSet -> Select -> Animation it is possible to make animated tiles that loop endlessly.
Is there a way to stop the looping? Or to set it not to loop? Or to find out when the last tile in the animation has been shown? Or when all tiles have been displayed? Or when a single loop has been completed? All questions are basically the same.
For any animation there is a checkbox to loop or not loop. There are signals for animation finished for non looping animations as well as telling the animation to stop via code.
once you figure out the animation player, go look at animation tree and tweens.
If you really want to use a tileset, i think you may need to estimate the time it takes for the animation tile to play and switch it to a different tile.