Nice work!

I noticed that you're caching `this` as a variable:

  var Blur = this,

And it looks like you're doing so to avoid scope problems in anonymous functions:

  Blur.img.onload = function(){
      stackBlurImage( Blur.img, Blur.canvas, blurRadius, Blur.width, Blur.height)
  };

I personally don't like this style. It makes it harder to read the code. If someone misses that `var Blur = this` line, they could get confused and either not use it, or use it incorrectly.

Instead, since you're using ES6, I suggest using the fat arrow:

  this.img.onload = () => {
    stackBlurImage(this.img, this.canvas, blurRadius, this.width, this.height);
  };

(I'm used to writing Coffeescript instead of ES6, so sorry if minor syntax details are wrong.)

This is largely a stylistic choice. You can feel free to do things however you want, and if it works, it works. But generally I prefer to make sure things are really clear, and that the Javascript features aren't obscured.