Flashing in circuit is not that easy with this chip. It involves some bankswitching and you need a programming voltage. The disadvantage of Flash chips is that they can only be erased bank wise. I don't know how many banks your chip has.
If it has only one bank, you will have to erase the whole chip before reprogramming is possible. This will also erase the bootloader! You will end up with an empty memory if there is an upload error.
Another problem with flash chips is that you can not read from them while programming is in progress. That means that you have to copy the bootloader software to RAM and execute it from there to write to the flash.

An alternative is to use the 29EE010. That chip is byte wise erasable and can be found on many PC main boards as bios chip. You can copy the contents of this chip to a normal 271001 and replace it on the main board of the PC. This has another benificial side effect: Virussus can not erase your bios chip anymore.
I don't know if you can read from the 29EE010 while writing is in progress. I don't have the specs here. So the copy to RAM trick might still be needed.