Wood thickness
I am wanting to make my daughter a baton case similar to what is shown. Her handle os 0.8" in diameter so I was going to use a 1" box core bit to make the slot for the handle. I was going to make the slot 0.5" deep on both sides. My question is how thin can I have the wood between the bottom of the slot and the outside of the case? I don't want to do more than 1/4" but I was wondering if I could go as thin as 1/8"? The shaft slot is getting a 1/4" box core bit about 1/4" deep. I am not worried about that one.

I think you will be fine at 1/8" if using hardwood.  You can garner bonus points by milling that slot on an incline, so that the baton lays parallel with the open face of the case.  

You should be fine. Just remember that due to the round shape, the 1/8" thickness will only be along a very narrow area.
I know the 1/8" will be a very narrow area I was looking to see what others thought. These are most likely going to be stuck in book bags so they will get some abuse.

I don't think I will be getting any bonus points. To get it to lay perfectly flat I would need access to the baton which is 3.5hrs away.
shaft slot should start out deeper than 1/4 if the handle is .08
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I should also ask how much space does flocking take up? I am planning on using the loose flocking material from Woodcraft.
I think you have a decimal off by one place. The handle is 0.8" in diameter not 0.08". The shaft is 1/8" so from the widest part of the handle to the edge of the shaft is 0.338" If I make the handle slot 0.5" deep and the shaft slot 0.25" deep then the distance between the bottom of the two slots is 0.25". This is less than the distance from the edge of the handle to the edge of the shaft. If I messed up my math please let me know.

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