If you want to make your own kaleidoscope prism effect in After Effect, you can use this FREE template to give yourself a head-start. It includes the fundamentals to design your own prism lens which can be further customized to suit your video, or you can just leave it how it is.
You have plenty of different options to customize and use the project file. Once you've replaced the placeholder footage with your own, you may need to mask out you subject to remove the background if the effect doesn't look clear at first. You can then adjust the RGB split effects and other VFX layers to better suit your scene.
There are several ways you can transition into the prism lens effect. The best way would be to either use a shake effect pr gradually increase the opacity of the kaleidoscope layer.