Does Emotional Intelligence (EQ) demonstrate the Flynn Effect?
The Flynn effect actually says that fluid intelligence is a function of modernization. This is shown as early as Luria's work during the introduction of formal education in rural Uzbekistan, and it can be still observed today in societies that for example do not allow women into formal education. 

In such cases one sees that male IQ has increased during the past decades whereas female IQ has not. Thus an argument can be made, based upon cross-cultural comparisons and taking into account differences of various groups within the same culture. 

For example between religious and not religious women in Israel -- the former do not serve in the military, the latter do, and this factor interacts with the male-female difference in IQ. 

So, in order to find an emotional intelligence parallel to the Flynn effect, the question is whether there are cultural factors that are rapidly introduced to traditional societies and produce measurable differences in emotional intelligence between groups that have a different degree to exposure to these factors.