Flightspeed is being installed. Use the home button or the application switcher to monitor the progress.
If this is the first Lightspeed app you install outside Apple's App Store your will need to confirm that you trust Applications from Lightspeed.
To do so, open this section of the iOS settings:
Settings -> General -> Profiles & Device Management -> Lightspeed POS Inc.
And tap on Trust "Lightspeed POS Inc" and Trust.
This will enables your device to run Flightspeed and any apps built by Lightspeed for Lightspeeders.