Outlook crashes after adding second account after upgrading to iOS 9 on iPhone 6
The only reliable way I had to resolve this issue was to delete the application and then reinstall it from the App store.

To do this, on the screen with the Outlook app, press and hold the icon until it starts shaking, then click the 'x' in the top left hand corner. Then go to the App Store and redownload the app.

You'll need to do the configuration of it again unfortunately, but it shouldn't take too long.