Hi, a quick google scholar search with "species richness" +dragonfly revealed at least three:
Kadoya, T., & WASHITANI, I. (2004). Dragonfly species richness on man‐made ponds: effects of pond size and pond age on newly established assemblages. Ecological Research, 19(5), 461-467.
Heino, J. (2002). Concordance of species richness patterns among multiple freshwater taxa: a regional perspective. Biodiversity & Conservation, 11(1), 137-147.
Clark, T. E., & Samways, M. J. (1996). Dragonflies (Odonata) as indicators of biotope quality in the Kruger National Park, South Africa. Journal of applied ecology, 1001-1012.
When I was studying damselflies and dragonflies I found some papers of Dra. Ola M. Fincke that were very useful: http://faculty-staff.ou.edu/F/Ola.M.Fincke-1/page2.htm
We estimated species richness using the Chao2 index in: Giugliano L., Hardersen S. & Santini G. 2012. Odonata communities in retrodunal ponds: a comparison of sampling methods. International Journal of Odonatology, 15(1): 13-23.