This is with avr-gcc and avrdude under linux with an Atmega1284p and AVRISP mkII! Adaption to your case (WinAvr, another Atmega, another flash-tool) will not be complicated...

adapt Makefile
- MCU_TARGET: Your atmegaXXX
- BOOT_ADR: in bytes not words!
- F_CPU: CPU Frequency (not critical. A higher value will work as well)
- SD_CS_PORT: Data Register of the SD CS pin(see the datasheet for your microcontroller)
- SD_CS_DDR: Data Direction Register of the SD CS pin
- SD_CS_BIT: Bit of the SD CS pin
- USE_LED: For debugging 0...deactivate or 1...active
- USE_UART: For debugging 0...deactivate or divider (UBRR) for baudate see http://wormfood.net/avrbaudcalc.php
update spi_pins.h with the SPI pins of your microcontroller if not already defined
if using USE_LED adapt LED-pins in asmfunc.S
if you want to add FAT12 adapt pff/src/pffconfh.h (default ist FAT16 + FAT32)
if you want to support lower case filenames adapt pff/src/pffconfh.h (default is uppercase)
if you prefer another filename instead of FIRMWARE.BIN adapt main.c
make (you may need to do "sudo apt-get install avr-libc gcc-avr")
set fuses: avrdude -c avrispmkII -p m1284p -U hfuse:w:0xda:m
- find high fuse in http://eleccelerator.com/fusecalc/fusecalc.php?chip=atmega1284p
flash: avrdude -c avrispmkII -p m1284p -Uflash:w:./avr_boot.hex:i -Ulock:w:0x3F:m

Put your sketch on SD card

in Arduino IDE go to File > Preferences and check "Show verbose output during compiliation"
compile sketch and find the location of your /tmp/buildxxx/sketch.cpp.hex
make bin file: avr-objcopy -I ihex -O binary sketch.cpp.hex FIRMWARE.BIN
copy the file into the root of an SD (FAT16/FAT32)
put it into the SD slot of your ATmega
reset it
it might already have happend!

Bootloader sizes

Compiled under linux for atmega328p / atmega1284p

3674 / 3724 bytes
3984 / 4034 bytes debugging with USE_LED
3992 / 4052 bytes debugging with USE_UART

Tested successfully on

ATmega168
ATmega328P
ATmega32u4
ATmega1284P
ATmega2560 (see issue #2)

Serial support - Help wanted

it should not be impossible to fit a normal serial bootloader (with automatic baudrate detection?) into the remaining bytes ... help is appreciated!

KISS

If you wish you can add CRC Check or versioning with EEPROM but I prefere to keep things simple. avr_boot will reflash your FIRMWARE.BIN as long as it is present. Is this a problem? No! It happens nearly instantly and only differing bytes are flashed really. You may consider putting your logic into your application and perform a CRC Check after the fact to inform the user and delete or rename FIRMWARE.BIN

Thanks to

https://github.com/per1234 - Boards Manager Installation and help with differenct MCUs
http://elm-chan.org/fsw/ff/00index_p.html
Wilfried Klaas for the MCSDepthLogger https://github.com/willie68/OpenSeaMapLogger
https://github.com/mharizanov/avr_boot
https://github.com/osbock/avr_boot
and others???

Alternatives

... call me stupid, but I passed several days debugging those - without success ...