No big deal. You design them like regular PCBs using Altium or whatever and follow certain guidelines. Typically one or two layers can be inexpensive. Search makers for their manuals and capabilities. You will need to be careful in specifying thickness and stiffener if you want to plug into an FPC connector.
Altium in particular has a feature that allows 3D folds so you can see what the finished product will look like.
Starting price is about $100 USD FOB for 5 or 10 pieces if you are willing to deal directly with Chinese suppliers.
Unfortunately rigid-flex is not nearly in that category yet, it cost several thousand USD last time I bought a smallish quantity (but worth it in that case). For that amount of money you can get very nice rigid boards with microvias, buried vias and many layers in a custom stackup.
I don't think flex boards with a huge number of layers are very practical- they will be too stiff, but you can make rigid-flex with the rigid part having many layers. I understand the different CTEs and other issues make it kind of hit and miss and they may have to iterate to get decent yield on the first run (and there can be a LOT of steps involved (it's even possible to design boards that cannot be manufactured because of the drill steps).
Sometimes it's recommended to put two flex cables (each with half the layers) overtop of each other to get a smaller minimum bend radius. You can do that with rigid-flex.