In the animated sprite if you go to the signals section you will see a signal "Animation_Finished".
This signal will happen when that animated sprite finishes its animation so you can link this to a function in a script to restart a new animated sprite immediately. when you click on the signal it will prompt you to link it to a function in a script so it isnt too difficult.
You can just link it to a function which restarts a given animation or you could manually emit a signal with the animation name in if you wish, this requires a bit more setup but basically you can do it as below.
For a signal named animation_finished inside an object named anim.
Objects tell anim that they are interested to know when animation_finished happens.
anim.connect("animation_finished", interested_object, "function_to_call")
Anim eventually notifies everyone.
(default nodes emit their signals automatically)