IQ must be not just genetic but heritable.

Yes, inherited genes play a large role in intelligence. Just like they do in everything else like skin color, height, facial features etc.

it would have to be known not just that IQ is an accurate measure of a person's potential

IQ is an accurate measure of a persons intelligence.

but also that it's an accurate measure of how their children will turn out

IQ distribution can be pretty wide for men, so the smartest man alive may be a Somalian man for all we know. However, we're not talking about individuals we're talking about the general population of various ethnic groups.

If you can't, then your entire argument falls apart at the seams: unintelligent people could still produce highly intelligent offspring, and vice versa.

My argument does not fall apart anywhere, we're talking about the general population and IQ averages, not exceptions.

9 times out of 10 people with low IQ will produce offspring that has similar IQ as their parents.

IQ would have to be causal of socio-economic circumstances, and not vice versa

How do you explain the vast IQ differentials between North Koreans and Somalis, or Sierra Leoneans and Somalis? Their socio-economic circumstances are very similar, yet Somalis have an average IQ of 68, Sierra Leoneans have an average of 91 and North Koreans an average of 106.

The Flynn Effect does exist but it is not as powerful as you suggest, around 60-80% of IQ is still inherited according to most studies. And the Flynn Effect can also go in reverse as it has done in Denmark for example. There the average IQ has gone down from 100 to 97 in the past few decades due to mass immigration.