"Is D-Cinelike just a flatter colour profile with less contrast (to capture more detail in shadows and highlights)?" Yes. It's closer to log color rather than linear. The big thing to be aware of in post production is to make sure you grade it to where you want it to be and possibly use their LUT to convert back towards Rec 709 depending on what you are looking for.
If you don't want to have to work on your color, don't shoot D-Cinelike. If you want the best recovery in highlights and more ability to adjust the tone, shoot D-Cinelike and spend the time to apply a color grade to your liking. (D-cinelike isn't so great in shadow unfortunately).
Personally, I always shoot D-log on my Mavic 2 Pro, which is similar in concept to D-Cinelike, though it has better shadow recovery and a bit more balanced, though slightly less cinematic looking without more effort to tweak it, but last I knew, D-log isn't available on the Mavic Air.
If you want to see some good samples, this youtube video seemed like it had relatively good comparisons of the 3.