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
This solution posted recently seems to be working out for people for dealing with gesture conflicts on pano / pivot. You might like to check it out.
Preventing the Pivot or Panorama controls from scrolling
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?
I found this works well for incorporating a slider on a pivot item:
LayoutRoot
Pivot
PivotItem
Grid
Scrollviewer
[Content goes here, I use another grid]
Slider
If I skip the grid and place the slider inside the scrollviewer it doesn't work. I stumbled upon this solution as I wanted to support landscape and still have the slider visible / usable.
You might be able to place your small UI segment for the gesture similar to where I placed my slider.