How thick is the flexible PCB that you are using? Could you put a flat flex connector on your board and design your flexible pcb to socket into it?
Hmm... As I type this I wonder if this will actually work. I would be interested in what someone who has used flex pcb has to say.
You can get free-hanging terminal blocks for FFC, but a quick check on Digikey revealed that these are only available for 1mm and larger pitches, which I imagine to be about the lower bound on the pitch of crimp housings for real wires. You might inquire with Tyco or Hirose about smaller pitches. If you can find these in 0.5mm pitch, this is the way to go for sure!
If you can't find a free-hanging terminal block, the best way to do this dependably, repeatably, and professionally is to build a breakout PCB. It doesn't need to be anything more than a connector and a couple of headers, but that will add some time and cost to your project. If you go to all that work, you might as well move the rest of your breadboard circuit to the PCB!
Connectors for FFC are almost always locking, so you should be able to buy a connector, put it on a protoboard/breakout board, and then solder to the connector pins. The pins will be small, but should be made of more durable stuff (Like solid brass or nickel, and likely gold plated) than the FFC.
I've soldered to these (Mounted on a circuit board, but otherwise similar) before, and I'll warn you that you want to do it with a cable clamped into the connector for heatsinking and stabilization. Otherwise, when you heat the pins and the plastic softens, the slightest twitch will push the hot pin through the soft plastic, and you'll get solder bridges and mangled plastic all over the place. I moved misbehaving pins back into place with tweezers and superglued everything after I was done, but, it might be helpful to let some glue harden in the bottom of the housing before you start. I couldn't get at the bottom of mine because it was already on the PCB.
Finally, you can get crimp/solder terminals for free-hanging terminal blocks individually. They look like this:
While you may have found it impossible to solder wires to the FFC, it's possible that a sturdier crimp terminal with a flat end will be easier to solder. Just make sure you crimp the wire in place first or heat sink your soldering job on the FFC when attaching the wire to make sure you don't mess that up after you get it working.
Whatever you end up doing, don't forget to the strain relief!
Best Answer
Manufacturers' crimp tools are precision-engineered for their connectors, and actually create a cold weld between the terminal and the wire. It's impossible to make a reliable connection without the correct tool. Distributors will usually make up cables for customers, using the correct tooling, even in prototype quantities.