Use quality tires with a Kevlar-type inner cords lining.
Have successfully used Maxxis Re-Fuse tires; last year a total of 5,000 miles of riding and 2 flats beween our tandem and my single bike.
One was a puncture from a tiny piece of steel wire from radial car tires and the other was a patch that came loose.
Live in the desert southwest, so lots of debris, cactus needles and a few goatheads + the usual road debris.
Tested solid 'airless tires' decades ago for a company. NO thanks! On super smooth roads no issues; bumpy /rougher roads lots of road vibration and crossing a cattle guard (if you live out west you know what those are) it actualy made the bike shudder.
Slime? Tried it years ago and not worth the bother/$$; it can mess up your valve stem and it may only seal some of the smallest of holes. Then if you do get a real flat the slime/goop is all over inside the actual tire and a mess; almost impossible to patch the tube too.
More thread is not necessarily the answer either, as debris can get stuck in the tire grooves and create a puncture.
Watch where you ride or even use old fashioned tire savers. And carry a spare tube and pump.
Just our experience in over 300,000 miles of riding.
Rudy/zonatandem