Follow along with the video below to see how to install our site as a web app on your home screen.
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I haven't tried different ones for comparison, but FlightView has worked well for me.
It keeps all the flight info for as many trips as I have planned (up to 3 months in advance) and allows you to make notes for each trip. It gives alerts for gate and time changes, and maps flights in the air.
I bought the paid version because I like it so much (and it gets rid of the ads, which really aren't that intrusive).