Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Bristol to Kingsport as you normally would.
Bristol (BRS) is the airport you will fly out of if you book a flight from Bristol to Kingsport. You should not have trouble finding flights to Kingsport from Bristol; the airport handles an average of 0 outbound flights to Kingsport per day. You should also have plenty of airline options to choose from since 1 airline has flights from the Bristol airport to Kingsport. It is only a 7.4 mi journey to Bristol (BRS) from Bristol’s city center.
This flight path from Bristol to Kingsport was viewed by 30 users in the past month. Keep an eye out for changes in search interest prior to high and low season.