You can view a feed of your own distances in a number of places:
In The Conqueror App:
Go into the Challenge. Tap on the right hand menu and choose the "Newfeed" icon (2nd from the bottom), Then change the Filter to "Just me" and you'll see all your distances. This will just include distances for the challenge you are viewing.
Tab the Bottom Left "Progress" icon and then at the top tap the right hand tab "View Distances". This will include distances for all challenges and if they were posted to multiple challenges they will appear multiple times.
On the home screen you can click the right hand tab "Activities" and this will break down your distances by exercise type.