For your application you normally do not send the file as one block of data - it gets divided up into smaller chunks and there is some error checking information added. One suggestion here is to use Xmodem protocol (search on the web) which is simple and sends the data as 128 bytes chunks. Therefore, you would store the 128 bytes of received data into ram (via the serial interrupt), check that the data checksum was correct, erase/write the data into flash then send an acknowlegement to the host. This cycle continues until all data has been sent and written. This method gets around the issues of timing in the ISR so you can run your baud rate as high as you wish. The ubiquitous Hyperterminal supports Xmodem.

Job done.