Okay, I'm going to make some assumptions in this post. If my assumptions are wrong, it may be beneficial to make these corrections to get this process to work. Assumptions being:
A.) You actually have the BIOS file you want to load.
B.) You have Flash-X on your Xbox
C.) You're familiar with the terms below
D.) You won't blame me if your Xbox blows up into a firey ball.
J/K, you should be fine.
1. Open you Xbox and move the DVD and HDD out of the way while still leaving them connected. It sounds harder than it really is. This will make sure you can load up fine and have access to your chip.
2. Boot up Xbox w/ working chip in place.
3. Once the dashboard is loaded, you should be safe to remove the chip and put the new (chip to flash) into the box.
4. At this point you have two choices:
A.) Disable flash protection. The center switch should be red when you do this.
B.) Leave flash protection on until Flash-X loads.
5. If you followed option A, you should have a menu listing. If you followed option B you will get a message that reads, "No X2 found or chip protected." Turning off flash protection should correct this.
6. Select "Load Bios" and find the drive that has the folder w/ the BIOS you'd like to flash. X2 chips use a 512KB BIOS so hopefully your files are of that size. I believe it is already.
7. Then, select whether you would like to flash banks 1&2, or 3&4. You have to kind of think about the banks this way, 1&2 are actually bank 1 on the switch whereas 3&4 are actually bank 2 on the switch.
8. Once your banks are selected, Press Y, then X to confirm that you want to flash this bank.
9. It will erase the bank and then flash the BIOS onto the chip.
10. Shortly after this process it should read "Done. Elapsed time X seconds," where X is the number of seconds it took.
11. You should now be back to the Flash-X menu.
12. Once done, turn flash protection back on, select the bank on the switch that you would like to load from (1&2=1, 3&4=2) and then Reboot.
If all goes well (and you flashed the correct BIOS,) your Xbox should load right up with your new BIOS on it.
Hope this helps.
