So far, gyms in my area flip so frequently that I haven't been able to hold more than one gym at a time when collecting my rewards. I know the reward for a single gym is 500 stardust and 10 coins.
Does this reward scale linearly with multiple gyms, or does it follow a different progression? I've also heard there might be some kind of bonus for holding a gym for more than a day, but haven't managed to do it. Is there a bonus for that (or any other kinds of bonuses)?
The reward scales linearly it's 500 dust and 10 coins per gym up to 5000 dust and 100 coins per defender bonus collection. You can collect your defender bonus if you haven't collected for at least 21 hours prior.
I have held gyms for multiple days and haven't seen any sort of bonus when collecting the defender bonus. Perhaps there is an xp bonus or something but I have never seen it in the journal so I doubt it exists.
I'm currently king of a level 10 gym, and have been for roughly 27 hours, I got no bonus other than the usual 10 coins and 500 stardust. So holding a gym for 24 hours just makes you feel special, and that's about it.
Apparently you have to go into the "Shop" and click on the shield in the top right corner. You can then collect a defender bonus every 21 hours from that point.
I have no Pokemon at gyms rt now so I haven't been able to test that