Connect kindle 3 serial port to epson printer's 8 pin mini-din serial port?
Not without level shifting. The Kindle's serial port uses TTL serial at 1.8V, whereas the printer's serial port uses RS232 serial (i.e, ±12V). Attempting to connect them together directly is likely, at a minimum, to destroy the serial pins on the Kindle's SoC.

The Kindle's internal serial port is primarily intended for debugging. It's probably best to leave it alone here; if you want to connect the Kindle to an external serial device, a better approach will be to use its USB port in host mode with an external USB/serial adapter.

The 8-pin serial adapter on the printer side is standard RS232 serial using an unusual connector. If you search around, you should be able to find adapters from this connector to standard DB9. (You may have some trouble finding them, as the computers that used these have been obsolete since the late 90s, but there are undoubtedly some still sitting in a warehouse somewhere.)



In re. edit: A 4 pin Mini-DIN port is most likely either S-Video or ADB, as you have identified. Neither one would be usable as a serial port.