From some chats a few years ago with EEs in the industry, eMMC chips -- as the "e" would suggest -- are embedded on the board and aren't meant to be removed once placed. To program these devices after-the-fact, the prototype units will usually load a header with maybe 6-8 pins, that breaks out the SPI lines and power. Then an ISP device would be used against that header -- with appropriate breakout board -- to load the flash image. Once the image passes final verification, it's given to the manufacturing line to load prior to being soldered down. The SPI lines usually suffice, trading off performance.
In one instance, I have seen a USB-to-SD card adapter that was rewired in a pinch, so that it could read out the image from an installed eMMC chip.