There are several ways to fix a bad BIOS flash. I think there are some few places you can order a chip already flashed with the BIOS you need, however that's kind of a waste as it's possible to fix the current one, since the chip itself isn't damaged (unless you really screwed up).
Most BIOSes have a non-writable section which contains code to boot from a floppy disk, even if you can't see the output or interact with it (in the old days, it could even run an ISA video card); I think in some cases you can even use a PS/2 keyboard, but of course you can't see what you're doing. Since this section is not overwritten even during a bad flash, it can still be used to reflash the BIOS.
Assuming you have a floppy drive, what you have to do is make a DOS boot disk, which loads nothing but the basic DOS system (clean boot), no himem.sys, no memory manager or other drivers. Then get the DOS BIOS flashing program for your particular BIOS brand and put it on the disk, along with the BIOS image file. You'll need to get the particular command line options for your particular BIOS flash program (google search can find them), but generally just the command like flash.com image.bin will work; in some cases, other options might be needed, since by default the flash program might not overwrite parts of the BIOS. The instructions that come with the flash program may also give you the correct options. Make an autoexec.bat file on the floppy disk with only that command line on it, and boot the PC with it. You should see the floppy being read, give it a good long time, at least what you expect a flash to take normally, and you should get a beep to tell you it's done.
If that doesn't seem to work, your other option is to use an identical mainboard, and flash the bad chip with that. To do this you boot the good system, pull the BIOS chip (which can be risky since you could damage the chip or the mainboard, and you have to do it live), and put the bad chip in and flash it. Then you could leave it in there and put the other chip back in the first board, or just swap them again; once it's flashed of course, you can turn the machine off to make it safer to swap them.
I believe it's also possible that you can flash the chip in a board that's not the same, as long as they use the exact same type of BIOS chip, just following the same procedure. You'd have to use the flash program's options to ignore errors probably, since it isn't the same BIOS that the system is currently running, but you can't do any further damage, once you shut off the good machine and put its chip back in, there's no difference.
