Arguing that the flynn effect shows that someone else should have a different opinion on the question of how much intelligence is heritable just shows misunderstanding of the meaning of the term of heritablity.

Otherwise it would be logical to say that all of intelligence is due to culture. Why? Let's say all individuals with IQ > 300 happen to be born past the singularity. Past singularity we have the technology to make people intelligent and therefore intelligence can't be truly innate.

Therefore modern biology defines heritability as the variance of a trait within a given population that's due to genetics. In it's essence the question of heritability doesn't only depend on genes but it also depends on the environment.

There nothing wrong with saying that the heritability changes over time. A society where every child can eat as much as it wants has probably a different heritability for IQ than a society where some children don't have enough food and other children who have wealthy parents do have enough food.