Soldering to flex circuitry can be accomplished in several ways. Flex circuits are prone to de-lamination, a direct result of excessive or pro-longed heat cycles, so whichever approach you choose for assembly, care must be taken when developing the thermal profile to ensure you avoid such damage.
For fine pitch devices, you may consider hot-bar technology which can fuse all leads simultaneously. In this case, heat remains relatively local to the device being applied.
You can also successfully reflow flex circuits as long as you observe thermal criteria for the flex assembly. Often when reflow soldering flex circuitry, a fixture or heat-sinking "mask" such as an aluminum template can be utilized to protect the un-processed areas.
This assembly method may work very well for your application where the connector area can be exposed, and remaining circuitry remains protected from excessive heat exposure.
While not necessarily suggested for bonding connectors, flex circuits can also be assembled using conductive epoxies. These materials are processed under curing profiles which are much cooler than the standard reflow profiles utilized for solder pastes, and as a result are much safer for the flex material.
Conductive epoxies/adhesives can have other drawbacks as well, so before proceeding, make sure you check with your material supplier on your specific application.