Did you type the bios name correctly?
Did you navigated, in the cmd window to the folder where atiwinflash and the bios file is?
This is what I did:
First I decompressed atiwinflash 2.0.0.2a (that includes atiwinflash.exe plus a bunch of other files most of them dlls) to G:\bios 3850\winflash.
Then I copied the bios file to that folder.
Then opened a cmd window
http://img140.imageshack.us/img140/7706/cmdze6.jpg
If you have a sapphire 3850 512mb, that is locked bios ver. 010.070 or previous, and if you can find a bios file for that card that is newer, go with it.
If you cant, then you can try a bios from another brand, but it may not work and in that case you have to be prepared for a blind flash or having to insert a pci card to reflash your 3850.
In my case I flashed my powercolor hd3850 pcs 512 with the gecube one that Greg_1 posted above and it worked.