iPad: export Keynote project to video
Keynote for iOS does not support this. Apparently Apple does not provide any mechanism for screen-recording (video) within iOS 7, and will not permit any third-party app that enables this. There have been some apps that can do screen recording on iOS 7, but they require jailbreaking the device, and are not authorized by Apple through the App Store. 

The only way that I know to achieve this is by one of the following: 

1) move your Keynote document that you created on iOS to Keynote on Mac OS X, which has a video export feature

2) If you have a Windows PC, you can use Reflector for Windows, which enables live video and audio recording of a "screen share" of what is playing on your iOS device. You establish a connection between your iOS device and your Windows computer, enable "Record" in Reflector, and then play back your Keynote document in full screen on your iOS device. You then have a video on your Windows computer that you can further edit.