I have a Pivot Control in my WP7 app that by nature responds to left and right swipes to move between the pivot items.
I then want to use the Flick Gesture on a User
The short answer is don't put a control which supports a gesture on top of another control which also supports the same gesture.
Please see this answer to a very similar question for a slightly longer response: WP7 Toggle switch in a Pivot control?