I purchased a 4-pack of 14 inch hanging baskets from Amazon. They have the fiber liners included. The plan is ferns and dipladania in them and hanging from the deck overhang. I am concerned about the liners being thin and I will get medium coming through when I water. I thought about putting a plastic bag in the basket and planting the plants in that. I'd poke a few holes in the bag for drainage. Or could I line the basket with newspaper? Any suggestions would be welcome. Thanks.

I have never had a problem with a liner for year 1. Depending upon light and watering frequency, I have got 2 or 3 years out of most liners.
I am doubtful about plastic because of not only limited water flow, but reduced air flow is also a problem.

I did a plastic bag because for me, hanging baskets seem to dry out really fast. Not sure how it worked, I gave them to my daughter where she was house sitting.
I think newspaper would last long enough to let the soil sort of
'settle in place' and maybe not leak so I agree with your logic on either of these.

I have used a layer or two of newspaper in the past with no issues; by the time it degrades roots have filled in. For annuals by the start of the next season when planting medium needs refreshing the paper can be, too.

Landscape fabric or window screen would be better options, without risk of surfacing in an ugly way (plastic,) or degrading to the point of uselessness too quickly (newspaper.)