You could put it in airplane mode during the flight or just ignore the call I guess.
The new Mavic won't take anything more than about 16cm long so that's up to 'large' phone, though you can use a tablet alongside with longer cable.
Since a lot of the info is shown on the (mavic) controller's own screen the smaller size is less problematic even if eyesight is not perfect. 

You don't actually needed a fully functional phone - an old one with no sim card would be able to download maps and perform updates on wifi at home.
Android phones and tablets work just as well, but the app is demanding and you need Quadcore and 2GB Ram, also at least Android version 4.0 (I think)

There's only one version of the app for phone or tablet, it is not particularly hard to use and a lot of the settings you only look at once then leave alone.