I remember you posting CAD screenshots of this a while ago, looks like the final assembly came out nice

How long is the PEEK section? Guessing 30-35mm from the photos? What's your anticipated temperature range?
I'm no mechanical engineer, but if you assume that the FPC is constrained to remain flat, then you could assume that the PEEK is perfectly rigid, and look at the modulus of elasticity of the FPC to approximate the maximum stress induced in the FPC for a given strain (really a limiting value, since the PEEK will take up some of that strain in reality). If the PEEK reaches the same temperature as the FPC during soldering, the strain can be calculated from the difference in CTE between the FPC and PEEK at any temperature T
1 as (T
solder - T
1) * ΔCTE * Length. But presumably the PEEK is not getting nearly as hot during soldering as the FPC, so you'd need to know or approximate the PEEK's temperature at solidification and calculate the dimensional change separately between that and the FPC to determine the strain. Also, the FPC isn't homogenous because the copper layer isn't solid across the length, and you have those metal reinforcements, with some sort of adhesive bonding them to the FPC, so there will be shear in that adhesive interface and...it gets a bit complicated. But you can still do some approximations via simplifying assumptions, like assuming the PEEK is perfectly rigid, and that the FPC *is* homogenous, and ignoring those reinforcements. Once you approximate the strain, you can determine the approximate stress from the modulus of the FPC, and finally compare that to the yield point of the FPC and see how close to failure it is. That would be for tensile failure of the FPC, in compression, I think your failure mode would be the FPC buckling away from the reinforcement, probably in one of the gaps between the copper sections. You could approximate the magnitude of that buckling from the strain.
Some rough CTEs for the materials in question just to get an idea:
PEEK 55 ppm/°C
Kapton 20 ppm/°C (value from Dupont's Kapton FPC datasheet, other forms are much higher)
Copper 17 ppm/°C
So there's a ΔCTE of about 35 ppm/°C between the PEEK and the FPC.