I've been going through my old photos and I noticed that I had a series that show how to wash and dry a kabuki brush. I was going to create a guide for someone on /r/MakeupAddiction/ but then I found the original video and figured there was no point. Since I have the photos lying around, here's my post about it but all credit goes to Dustin Hunter. It's a great video and a great idea, so I suggest you watch the whole thing.
I now store my kabuki brushes in this manner so the pictures I have are of a dry brush. Trust me when I say though, this method is very easy.
1. I use paper towels because they are closest to my sink which is where I wash my brushes in the first place. After I wash my brush, I roll it in a sheet of paper towel. Position it in the center of the sheet to assure there is adequate room at the top and the bottom. (You don't have to assure there is room at the bottom unless you plan on changing the storage method).
2. Wrap it up!
3. Slide it into an empty toilet paper roll. For future purposes, you should actually keep a few of these around. Not only are they great for drying and storing kabuki brushes, they are great for resting sponges so they can dry out.
4. You can now stand the kabuki up -- with adequate padding at the top by the bristles, you can allow it to "stand on the bristles" since now it won't hit the hard surface.
5. My brush was already dry so I can now toss it and store it in any which way I'd like, which means this is also great for travelling.