you can clear out the existing emmc content from your kali sd by using terminal or disk utility, gparted, etc.
what do you want to put onto your emmc? excluding OS options that have sd-to-emmc imgs, most imgs can be written directly to the emmc. so you could feasibly put a copy of the kali img (just using it as an example) onto your sd kali, as a downloaded file, open disks, erase the emmc, then restore the kali img to the emmc after. then you should be able to reboot/shutdown, pop out the sd, and boot into your new os on the emmc.
what do you want to put onto your emmc? excluding OS options that have sd-to-emmc imgs, most imgs can be written directly to the emmc. so you could feasibly put a copy of the kali img (just using it as an example) onto your sd kali, as a downloaded file, open disks, erase the emmc, then restore the kali img to the emmc after. then you should be able to reboot/shutdown, pop out the sd, and boot into your new os on the emmc.