If your proofing basket or basket liner is new or just washed, make sure you flour your dough thoroughly before placing it in the basket, and that you flour the basket/liner quite thoroughly, too, even rubbing flour into the basket/liner surface.
Rice flour is especially resistant to sticking, and many bakers use it in their baskets alone or mixed with all purpose flour. Other less common options include using a layer of bran flakes, or for seeds or dried herbs for specialty breads.
Ideally, you’ll almost never wash your basket or basket liners, and they will become seasoned with a layer of flour. I think of this seasoning as backup dried sourdough starter or dried yeast. Washing isn’t necessary unless you’ve just had a sticking episode and need to scrub away chunks of dough that would dent the surface of your next loaf. Always allow your proofing basket to dry thoroughly before storing it so it doesn’t get moldy.
If you do find yourself with an extra wet and sticky dough, you can always use parchment paper in the basket as a one-off solution. I like to crumple the paper in my hands first, so it doesn’t have pointed folds that press into the dough.
You can find more tips on preventing sticking in these forum threads.