I think double typing issues have been discussed before. They,as I remember, have been solved by turning off the Zagg; turning on and off Bluetooth in Settings>General; "Forgetting" this keyboard; then restarting the whole thing re-pairing, etc. See if that works.
Tried that....no real luck. Sometimes I don't get the double typing, but 8/10 I do. I've written to Zagg, just waiting to hear from them.