Using the keyboard to fly the plane requires a bit of setup:
First go to the Controls page in Infinite Flight settings. Make sure you are on the Axes tab.
Tap on the second column next to “Roll”, and press and hold on the left arrow key.
Tap under that next to “Pitch”, and press and hold on the up arrow.
Tap on “Throttle” at the bottom and press and hold the D key.
The page you are looking for looks like this: