Can Blackfin DSPs boot from 'any type' of SPI external flash?
Yes, the Blackfin "just knows" that it needs to issue a read command followed by an address (all zeros) in order load software from external SPI flash. Devices from different manufacturers (mostly) use the same set of commands.

The code that does this is stored in a small ROM inside the Blackfin chip itself. You have to dig for it, but Analog Devices usually has the source code for that ROM hidden away somewhere in the library files that come with the software development tools, in case you want to look at it.

I have had occasionally needed to work around bugs in the ROM bootloader with respect to specific SPI flash devices by creating an extra stage of bootloading for my project. I use the ROM bootloader to load a second-stage bootloader from the SPI flash, which then loads the application code. The second-stage loader is mostly a copy of the ROM bootloader, but it is constructed to live within the limitations of the ROM code, while also fixing the bug related to getting the application code loaded.

If you're interested in the gory details, I wrote a Circuit Cellar article about it. The article itself is not available online, but the associated archive contains the source code for my replacement bootloader, and the comments there explain exactly what the problem was.