Check the link that I provided for burning the bootloader with the Arduino IDE. I believe that it points you to the location in the IDE file structure that has the various Atmel bootloaders.
After much research, I managed to load the bootloader unto the APM2560 using my $4.95 usbasp device connected to the SPI connector on the APM2560. I used avrdude 5.11 in the windows terminal to set the fuses and load stk500boot_v2_mega 2560.hex to the APM2560. There were SCK and verification errors but when I connected it to Mission Planner it uploaded APM 2.7.3 without problems. Conclusion, 3DR must have shipped the boards without bootloaders. I sent an email to their help desk on Sept 28 and still have not heard from them. I learnt more than I wanted to about flashing and would prefer to spend my time tuning PIDs!!
I think there is more to the missing bootloader than you might think. I am in the same situation here. But when I finish putting bootloader and upload APM firmware. I notice that the LEDs in the bottom board are different. Usually with APM1, there are 3 LEDs that are always on, red, blue, and yellow. Now PPM and MUX LEDs are always off (Blue and Yellow LED in the bottom shelf). Only the red LED stay lid. So I connect Mission Planner to this APM1 to find that there are no radio input even though I connect the R/C receiver to APM1. My guess is that they might miss PPM/MUX firmware on these boards too.
You have to use both ISP ports. One for the 2560 bootloader and one for the 328 bootloader. Then you have to load the 328 with PPM/Mux firmware.
Just a thought.
I had the same issue. No boot loader in Mega2560 and no PPM firmware in the PPM chip. I had to flash both and now it works fine. I have AVR Dragon, which I used to flash the bootloader and the PPM firmware.