For anyone else experiencing similar issues with the blend modes, blendMode: 'ADD' and blendMode: Phaser.BlendModes.ADD both work for me on both Firefox and Chrome. I managed to get the sky and red particle asset from https://github.com/photonstorm/phaser-examples/tree/master/examples/assets and downloaded 'assets/sprites/phaser.png' instead of 'phaser-3-logo.png'. Hopefully this information helps someone.
Seems that when you try to load local images and later on this.load.setBaseURL it seems to append the URL even to previously loaded ones. Description of this function states otherwise (that it adds URL "...from this point on..."). Anyone had such issue?
For those having problems with the ADD blend mode. I downloaded the phaser.js from the main site and the files from those locations. I doubt the files have anything to do with the problem at hand, because everything worked fine when I used add as the blend mode (all lowercase).