Kindles and Kobos aren't USB peripherals by themselves
The both use the g_mass_storage (or composite maybe?) gadget driver in the Linux USB subsystem. They expect a USB host on the other side.
Probably it is doable given your phone acts as an OTG A-device when you attach an usb memory stick. You need to check that your phone is supplying enough power on the Vbus pin (+5V) to your kindle and yet enters in host mode. Some OTG A capable devices deliver power to a certain degree (which is fine to charge the other end) but then fail to enter USB host mode.
Maybe you can try with an
external powered USB OTG adapter