How do I design my own FFC cable
If all you need is a straight FFC then you can just buy a pre-made one, Digikey has a few sizes and pitches, but other vendors may have an even larger selection.

If instead you need an FPC (Flexible Printed Circuit) where the wires cross, then I would suggest to use any free CAD tool such as Kicad.
You will have to draw a schematic with two connectors (one for each end of the cable) and specify how these two connect to each other.
The next thing that you need to know if what pitch the pads of the FPC should be spaced, and ideally this information should come with the datasheet of the connector where you intend to insert the cable. In the datasheet you will also find the details of the mechanical buildup of the flex, which include the thickness of the ends that goes into the connector as well as the suggested coverlay thickness.
Once you have these details, you have to draw in the mechanical outline of the FPC, place the two components and connect the traces.

In general terms if you have never designed a PCB it will be really hard for a beginner to design an FPC.

An FPC is usually built on a base material which is Polyimide, a layer of copper, which is etched and over that a thinner layer of Polyimide called the coverlay, which serves the purpose of protecting the traces. Any exposed metal remaining, such as the pads for the connectors are plated in order to protected from oxidation.
If the FPC needs to be double sided it will have two layers of etched copper and two coverlays.

If all this is too much for you, I suggest you find an experienced PCB designer who can do this for you; there are plenty of PCB designers online who can quickly design and prepare a datapack ready for manufacturing.