Sugru is great for this kind of thing. Available on Amazon.
Although looking at your pic again--Sugru hardens to a firm state, so it might not be great for the middle of the cable. It's better for frayed cables right at the connector, essentially creating an extension boot like a strain relief. For the middle of the cable, possibly you could do the type of shrink wrap made for mid-cable, where it wraps around (vs the typical closed sleeve type). That will bend a bid, but still stiffer than the cable was without it. I'm hard pressed to think of a solution that will cure to a truly flexible state.
Thanks, Charles. I hadn't thought of combining two different solutions to maintain some flexibility. This is a cable for an old Red camera so it doesn't need total flexibility. I appreciate your expertise.
BTW, I just got an email about the Tiffen Tech Day. It was fun to see your name on the program, along with names like Cundey and Hurlbut. These are the times that I wish I was in LA.