This is not an unreasonable presumption on a priori diminishing marginal returns grounds. For example, in recent decades, life expectancy gaps between countries have mostly narrowed (except during the worst AIDS years in Africa), because traditionally rich countries have had diminishing returns at improving life expectancies compared to traditionally poor countries.
But, there's not much evidence of IQ racial/ethnic gaps closing in the real world: gaps in IQ are notoriously intractable. So, just eyeballing the data over the decades suggests that the Flynn Effect is about the same size for all racial/ethnic groups, with possibly Asians having a larger one.
Intelligence. 2010 July 1; 38(4): 367–384.
The Flynn Effect within Subgroups in the U.S.: Gender, Race, Income, Education, and Urbanization Differences in the NLSY-Children Data
SiewChing Ang, Joseph Lee Rodgers, and Linda Wänström
Although the Flynn Effect has been studied widely across cultural, geographic, and intellectual domains, and many explanatory theories have been proposed, little past research attention has been paid to subgroup differences. ... These prior findings suggest that the NLSYC data can be used as a natural laboratory to study more subtle FE patterns within various demographic subgroups. We test for subgroup Flynn Effect differences by gender, race/ethnicity, maternal education, household income, and urbanization. No subgroups differences emerged for three demographic categories. However, children with more educated (especially college educated) mothers and/or children born into higher income households had an accelerated Flynn effect in their PIAT-M scores compared to cohort peers with lower educated mothers or lower income households. We interpret both the positive and the null findings in relation to previous theoretical explanations.
... Until the current study, this finding could be explained by a differential Flynn Effect in which minority scores increased at a steeper rate. However, we found no interaction in our data; the three different race categories each showed substantial FE’s, but they also tracked closely to the same consistent increase. The absence of race differences in FE patterns also has implications for the various other theories. If FE patterns in the NLSY-Children emerged from within the family, or were related to average family size (e.g., Sundet, Borren, & Tambs, 2008), ethnic differences in family culture and family size could potentially create differential FE patterns; but those differences were not observed. If average educational quality is lower for minorities, this could lead to differential FE patterns; again, this finding did not obtain. As for gender, theories that are silent with regards race differences in FE patterns are consistent with the current findings, including the nutrition hypothesis, testing artifacts, and heterosis. ...
In conclusion, we now know new and important features of the Flynn Effect, at least the FE found in U.S. data from the past two decades or so. The effect itself is strong and consistent, but we found no differential gender or race FE, nor was there much of a differential urbanization status identified. The positive finding of a differential FE in relation to maternal education (and at a smaller level, household income) at the older ages is suggestive of some of the dynamics of the process leading to the Flynn Effect.