How to burn multiple FPGA
An FPGA (aside from some specialty products) doesn't store its configuration after power is removed. It must be re-programmed every time it is powered up.

Most FPGAs include dedicated logic to connect to an EEPROM on the same board and automatically configure the FPGA from data stored on the EEPROM after each power up. If you use this kind of FPGA, your problem is now how to program a bunch of EEPROMS to be stuffed on the boards with your FPGAs. 

For this, gang programmers are certainly available. You can also pay a service company to program your EEPROMs for you. 

But they might not be economical if your production volume is less than 100 units or so. Instead, you can use the regular in-circuit programming facility of your FPGA to program it to a design that routes signals from the in-circuit programmer through the FPGA to program the EEPROM. The major FPGA vendors build this capability in to their in-circuit programming tools so you might not even be aware that this is what you're doing.