What is the flashback in episode 14 of Ranma referring to?
I think you may instead be referencing episode 15, as this episode introduces Shampoo and has a flashback to the Martial Arts Figure Skating battle, which was originally planned to be air before this episode.  

Two episodes were cut from the first season, Wikipedia notes the reason as there being a sensitive feeling of the title and theme of the specifically the first of these episodes (The Abduction of P-Chan), due to many kidnappings happening in Japan during that time. 

These episodes were later inserted into season 2, which is where the clips come from.