Do not switch to Legacy BIOS. Keep UEFI enabled and Secure Boot disabled. Kali doesn't support secure boot as of now.
If it's your external SSD, I'm assuming your non-removable storage is HDD. Grub bootloader is installed in EFI partition of your hard drive.
In your UEFI settings, look for an option to add entry of bootloader in your boot menu options. PCs also have option to Boot from EFI in boot menu options. Look for either of the option.
Post screenshot of UEFI settings and boot menu options on imgur if you cannot find it.
I've also created a post to install grub bootloader in removable drive for portability but for this you must have knowledge of how to boot from EFI which is easy to learn by playing with UEFI settings
