I keep hatching wurmple with the run away ability, but every one that evolves into Cascoon/Dustox has shield dust. The parents are two Beautifly with rivalry. Does using Beautifly have some affect on keeping the HA?
It is because of Silcoon and Cascoon not having any HA. When the Wurmples evolve, they lose their HAs and they are stuck with Shed Skin. After they evolve into Dustox, they love Compoundeyes and are stuck with Shield Dust.
This is because when Wurmple evolves into Silcoon/Cascoon, it loses it's Hidden Ability because Silcoon and Cascoon don't have a Hidden Ability. Since it has it's normal ability, when it evolves again the Dustox will have it's normal ability, like it previously did.
You obviously got the Beautifly from a Friend Safari.
The only way you can get a Hidden Ability Dustox is to transfer one from B/W. Sorry.
Hope I helped. :)