I've never seen a chest in an abandoned mineshaft on Pocket Edition, although there is supposed to be at least one in each mine, therefore making it a bug. The stronghold storage rooms (the rooms with cobblestone and oak wood planks) shares the same bug. Normally, in PC, a chest can be found if you climb the ladder that contains things like apples and iron ingots, yet in Pocket, there is nothing.

This is clearly an issue rather than an intended feature, as all the other editions containing these structures generate these chests (minecarts with chests, in the case of an abandoned mineshaft) normally. If they couldn't add those, why not add normal chests into the mineshafts as a placeholder until the minecarts with chests are added?

And by the way, stronghold corridor and library chests generate as normal in PE.