GnuBee PC has a 32MB SPI flash chip which contains 7 parts; u-boot, u-boot-env, factory, firmware, kernel, rootfs, rootfs_data.

Upgrading the firmware will replace the content of the firmware, kernel, rootfs, and rootfs_data. This procedure does not require any specific OS and only needs a USB storage device.

    Format the USB with FAT32 (aka DOS) file system.
    Copy the desired firmware to the USB drive and rename it to gnubee.bin
    Eject the USB drive and plug it into GnuBee
    Power on GnuBee
    While loading the new firmware the Lower LED will give an indication or reading/writing:
        fast blink = read
        slow blink = write
        solid = done. (This may take several minutes.)
        Flash progress can be viewed over UART
    ~1min to read, ~2min to erase, ~2min to write
    When the upper LED changes from off to solid on, power off GnuBee
    Remove the USB drive

Debian is a popular general-purpose GNU/Linux distribution. It will require additional software installation step after flashing the firmware.
Base firmware image

    Download the latest firmware from http://neil.brown.name/gnubee/ and Install it
        http://neil.brown.name/gnubee/gnubee-6.1.1-gbpc1.bin for GnuBee PC1 (2.5" drives)
        http://neil.brown.name/gnubee/gnubee-6.1.1-gbpc2.bin for GnuBee PC2 (3.5" drives)
    After firmware install, insert BLANK storage (SD, USB, SATA) into GnuBee for debian OS
    Hold the black button while switching on power until you see a 1:4 blink on one of the LEDs and it will enter rescue mode, configuring the network to listen for an ssh connection
        Black network port uses IP address 192.168.10.1 and runs a DHCP server - connect your computer to BLACK
        Blue port uses DHCP to get an address - connect BLUE to your router/switch/network
    Connect via SSH to GnuBee
        username: root
        password: GnuBee
    Set up storage specific to your install (RAID, etc)
    In rescue mode you can use debootstrap to install a fresh Debian installation.
        The `config` script does much of the work


U-Boot 1.1.3 (Aug  7 2017 - 16:23:41)

Board: MediaTek APSoC DRAM: 512 MB

Config XHCI 40M PLL
******************************
Software System Reset Occurred
******************************
MediaTek SPI flash driver, SPI clock: 45MHz
spi device id: 1 2 19 4d
find flash: S25FL256S
*** Warning - bad CRC, using default environment

============================================
MediaTek U-Boot Version: 5.0.1.0-6
--------------------------------------------
ASIC MT7621A DualCore (MAC to MT7530 Mode)
DRAM_CONF_FROM: Auto-Detection
DRAM_TYPE: DDR3
DRAM bus: 16 bit
Xtal Mode=3 OCP Ratio=1/3
Flash component: SPI Flash
Date:Aug  7 2017  Time:16:23:41
============================================
icache: sets:256, ways:4, linesz:32, total:32768
dcache: sets:256, ways:4, linesz:32, total:32768

 #### The CPU freq = 900 MHZ ####
 estimate memory size = 512 Mbytes

 Reset MT7530
set LAN/WAN WLLLL
(Re)start USB...
USB0:   mtk-xhci: init hccr be1c0000 and hcor be1c0020 hc_length 32
Register 300010f NbrPorts 3
Starting the controller
USB XHCI 0.96
scanning bus 0 for devices... 3 USB Device(s) found
       scanning bus for storage devices... 1 Storage Device(s) found
reading gnubee.bin

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25749095 bytes read
## Checking image at 8e000000 ...
   Image Name:   Linux Kernel 6.5.1
   Image Type:   MIPS Linux Kernel Image (uncompressed)
   Data Size:    25749031 Bytes = 24.6 MB
   Load Address: 80001000
   Entry Point:  807f303c
   Verifying Checksum ... OK

 Copy 25749095 bytes to Flash...
erasing flash
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writing flash
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erasing flash
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writing flash
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Done!
25749095 bytes flashed
Firmware upgrade complete
Remove USB drive and reset board