Is there any way to sniff USB traffic between an Android app and a connected device, like a drone controller?
On a regular non-rooted device this is impossible.
On a rooted device it might be possible (but I would not know how). The common Linux solutions for capturing USB traffic require a special kernel module. If your kernel has no module support this would require to build a custom kernel with the USB sniffing kernel module included).
In both cases you still have the possibility to perform a man-in-the-middle (MitM) attack on the USB connection, e.g. by placing a special device in between that allows you to access the USB traffic on "cable level":