They're calling it the "BK Kitchen Tour + DIY Burger" and there are limited 2-hour sessions available that require at least 10 participants to proceed. It costs $8 SG (~$5.68 US) per person for ages 12 and under and $10 SG (~$7.10 US) for anyone else. The price includes the do-it-yourself burger, a small drink, and medium fries so you're basically paying for a combo and getting a free tour.
The burger can be made with various patties, sauces, and other ingredients.
If you happen to be in Singapore, you'll have to contact the company via email or phone to get the ball rolling.