I was trying to install my iphone application from testflight.
It installs perfectly on few devices but in some after installing about 80 percent it gives an error Unable to download application, <my app> could not be installed at this time
I am able to find out the reason for, why is it so?
Here’s a screenshot:

clear your cache and cookies in Safari, make sure your device is in provisioning profile and provisioning profile is installed on the device.
If everything mentioned above didn’t help, try to create a new build with higher build number and try to distribute your app again