If so then daaaaaaang, Hawlucha became more dangerous.
Yep. It'll activate. :D
Hope I helped. :) Source
Yes it activates because since unburden doubles a Pokemon's speed when the held item is lost, fling throws the item at your opponent and gives them damage so the unburden ability will be activated.
Source: http://bulbapedia.bulbagarden.net/wiki/Unburden_(Ability)
http://www.smogon.com/bw/abilities/unburden Hope this helps.