It will work normally like with any other avr programmer.
You will have to figure out for yourself what pin on your programmer is which connection, but normally it should be an ISP. If so, the different connections are like in the following picture:
Now you have to google for the datasheet of your microcontroller (the biggest flat chip on one side of the ESC, should be something with atmega).
Now you have to find all the 6 pins like in the small diagram in the picture above. If you've found the pins that have those connections, use a multimeter/multitool to check for direct connections on your ESC layout where you can solder on to. Don't use small resistors, or you will destroy the ESC, look for soldering points of bigger parts, solder pads or places specially made for flashing (sometimes Mosi, Miso and SCK have special soldering points for easier flashing).
To be sure, check out this thread on RCG and look for your ESC and it's connection points:
Solder some cable to those points and connect them to the corresponding pin of the avr programmer.