In general when looking for the cheapest flight to Billund, try to book your flight during the month of September for the best deal.
From most locations, booking your flights to Billund around 26 days prior to your departure date finds the best deals.
From most locations, the cheapest flights to Billund are found on a Wednesday. Booking a Saturday departure is usually the most expensive.
On average you can find the best deals on plane tickets to Billund when looking for flights with morning departure times.