The easy way is importing a video or image sequence with movement created in other software.
(the same button you use to open a image you can choose a video or sequence of images)
To animate with the black and white image you will need a more complex shader and probably drivers to control the parameters of position of image.
You can create some nice animations by adding some noise to the UV mapping like this
Changing/animating the X location in the noise texture mapping node will distort kind of like a wind in one direction which I assume is what you are trying to achieve
If you want to make the distortion less at the bottom you can multiply the noise offset by the V coordinate, that way the bottom of the plants stay still while the rest is animated
that is the point, i realy want learn blender more technicaly not to make anything.
that is so incridble. how do you guy learn this