Ahhh so! Thanks, Mayhem - I guess I don't get to do extra searches.
Actually, if you don't mind diving into the middle of things, do a Google search for "change kindle user agent" and then just spoof-it to make Bing think it's a smartphone instead.
I have no idea as to your technical prowess but, if the previous sentence made any sense to you then you can get the extra 10 points per day by spoofing.
Then go to bing.com/rewards from your Kindle and login using one of your outlook.com accounts or FB, then go to the dashboard and you should see the mobile search points.
I have another post on the main Bing Rewards Bot thread I just posted for Mayhem (kinda long-ish) but if you also have 5 Bing accounts and want to claim all 5 accounts from the exact same device (user-agent), you might want to think about using different "user-agent" strings per account so that Bing doesn't ban any of your accounts, that's what I'm trying to prevent myself.
Let me know how you do with the Kindle.