I have raspberian installed on my RPI3. Can i use airmon ng to monitor other wifi networks, and still be connected to my android phone's wifi network? My goal is to keep vnc on wifi network running while using airmon ng.
It is possible, but it depends if your wifi dongle have this feature, some of them allow both states.
But in this case (Using rasp wireless lan card), you probably need another Wifi module or a Usb dongle, one of them connected to the AP and the other one listening in promiscous mode.