The closest major airport to Barksdale Air Force Base is Shreveport Regional Airport (SHV / KSHV). This airport is in Shreveport, Louisiana and is 15 miles from BAD. If you're looking for domestic flights to SHV, check the airlines that fly to SHV.
Travelmath helps you find the closest airport to any city, as well as a list of smaller local airports. You can use these pages to plan your trip and figure out the easiest way to get to your destination. Many times there are multiple airports near the city you want to visit, so you can often find a cheaper flight into a different airport. This is especially useful if you are getting a rental car, since it might be better to drive a bit farther in order to save money on airfare. If you're booking an international flight, you probably want the closest major airport, otherwise if you're a pilot you may be looking for a local airport. Use this tool along with the flight distance pages to plan your travel.