One of those questions that is relevant and interesting.  Akachi and Canning use the DHS surveys and trace how birth cohorts have attained different height.  Interestingly, in the simple time trend heights are steady (on average just under 160 cm or about 5’2″).  Only a handful of the 20 countries have significant time trends, and these are small.  Of course, there are mortality selection effects, and for earlier cohorts stunted children may have been more prone to die and not reach adulthood.  Once country-level GDP and infant mortality are controlled for, the trend in height appears to be downwards.  Unfortunately, Africa is one of the only world regions with declining per capita GDP for several decades, followed by rising GDP, so interpreting the conditional time pattern is hard.

This negative time dummies effect may reflect omitted variables that negatively impact height and is indicative of a negative trend in the biological standard of living in Sub-Saharan Africa. It may also reflect a changing relationship between health as measured by mortality rates and stature.This suggests the need for a more detailed measure of health than mortality rates,particularly measures that reflect the disease environment and morbidity, in understanding the evolution of heights. However, the interpretation of the time effect remains an open question.

There is lot of variation between countries (and I imagine between ethnic groups).  The Sahel countries are quite a bit taller.  Madagascar quite a bit shorter.
Akachi, Y. and D. Canning (2007). “The height of women in Sub-Saharan Africa: The role of health, nutrition, and income in childhood.” Annals of Human Biology 34(4): 397-410.