There is no BIOS layer in the Amiga, nor is it correct to refer to the kickstart as a BIOS.
A BIOS is a masking layer between hardware and your software, basically just a translator that keeps all hardware looking the same to your software, no matter what IDE controller or SCSI controller you have for your hard disks, etc. Almost like a driver collection but they are a lot more generic and do a lot less than an OS native device driver would.
The Kickstart is akin to if the Windows kernel and some of the drivers came off a ROM chip on a PC. Coreboot
is the closest thing to Kickstart you can get on a PC. :-)
Oh, and ever since 3.1 came, I called the Amiga's OS, AmigaOS. :-)