When starting with any kind of animation you should lookup the principals of animation. The same motions that make a character walking look interesting, makes particles interesting.
Math waves also looks good, with games like the above you will need to look into rhythm. Both these can be used with out any animation knowledge or animation software, because you only need sprites and math functions.
I wouldn't recommend photoshop for animations, there is a lot of free software that can do better and is more detected to animations. If you have a lot of money you can also buy animation software, although for making games you won't need this level of software.
More importantly like I mentioned above this can be made with out any animations, in fact I believe the games you are using as references don't use any sprite sheets. Using some simple math you can achieve all of the above effects.
Lookup: vector math.
I believe the whole idea behind Flow was the art of vector math combined with simple game rules to create a living world. At least from a artistic point.