While Tom Landauer died in 2014, so he won't be responding to your question, he was an excellent text researcher. You might be interested in his work at the University of Colorado but particularly in work he did for Pearson on developing Pearson's measure of text complexity. This looks like a measure you could use in the context that you are interested in.
Hm, some ideas can be taken from the existing measures...
Complexity – one may use the Automated Readability Index (ARI). At the output ARI
gives a number which approximates the grade level needed to comprehend the text.
Richness of vocabulary can be measured by using the Yule’s I index.
But in all cases you should adjust such measures to your precise case... tweets are short, agrammatical and so on. Perhaps one has to store several tweets with the same author in order to have a statistically reliable picture and to apply the measure to the author and not to the tweets?