Interesting work. This section caught my attention...
"Notwithstanding the aerial innovations documented by putative non-avian dinosaur fliers as early as the middle-late Jurassic (Hu et al., 2009; Dyke et al., 2013; Xu et al., 2015; Dececchi et al., 2016), the 150-million-year-old _Archaeopteryx_ is broadly regarded as the earliest example of flapping flight capacity (Burgers and Chiappe, 1999; Wellnhofer, 2008), albeit limited to short bursts (Serrano 2015; Voeten et al., 2018). While such an aerodynamic breakthrough might have evolved earlier, compelling evidence for the attainment of sustained flapping flight first appears at about 131 Myr, as it is documented by several avian lineages (e.g., confuciusornithids, enantiornithines, and early ornithuromorphs) from the Huayijing Formation of northeastern China (Zhang and Zhou, 2000; Zhang et al., 2008; Wang et al., 2015)."
The hypothesis that miniaturization preceded flapping flight is uncontroversial, and makes perfect sense (e.g., Turner et al., 2007). However, although _Archaeopteryx_ is broadly regarded as the earliest *known* example of flapping flight, the _Archaeopteryx_ it's possible that its ancestors in the Middle Jurassic were already capable of some form of flapping flight. The authors do allow for this ("such an aerodynamic breakthrough might have evolved earlier"), but it's possible that the emergence of flapping flight occurred when (according to this study) AOC and air density were higher, in the Middle Jurassic. Also, certain anchiornithids might have engaged their wings for flapping-based aerial leaps during the same interval, although true flapping flight (even short bursts) was probably beyond their capacity.Â
For long-armed/'big-winged' paravians, miniaturization certainly facilitated aerial locomotion; but I'd go further and suggest that the opposite was also true -Â
aerial locomotion
facilitated increased miniaturization in certain lineages. Aerial leaps allowed small cursorial theropods to clear obstacles on the ground, and this engendered a positive feedback loop that accelerated the evolution of powered flight. So miniaturization and flapping-based aerial locomotion might have coincided.
The later increase in AOC and air density is hypothesized to have played a major role in the diversification of early pygostylians during the Early Cretaceous, including Jehol birds. This is also the time and place of _Microraptor_, so maybe the same conditions helped get microraptorines into the air, if (as seems entirely possible) they were true powered fliers.