Burning hex files into multiple micro-controllers at a time.
Is there any way to burn multiple microcontrollers at a time just using 1 programmer?


If your micro uses JTAG as its programming interface, and you can arrange to connect the micros you want to program together in a JTAG chain, you may be able to do this. I'd be surprised if the software that comes with the vendor's programmer supports it, though. 

Some other options:


Get a gang programmer and program the parts before loading them on the board.
Make a pogo-pin fixture to speed up connecting and disconnecting the programmer from the board, and speed up your existing process.
Hire a programming service to program the parts for you. Your assembly vendor can probably either do this or recommend a third party to do it. This can be reasonable for batches of maybe 50 or 100 or more parts.
Order the parts pre-programmed. This is probably only reasonable for batches of 5,000 or more parts.