Dynamite is a very destructive and dangerous thing, so it's delivered in small batches via secret channels. You can get it:
 
- as a reward for quests,
- by watching explosive ad videos from Boom Guy (he comes rarely, but when he does it's when you need him most),
- in the gift box for playing 20 days in a row,
- by winning contests from Klondike citizens on our official pages: 
The bravest will also find it in some treasures in expedition lands (all lands except for the one where your farm is).
 
By the way, in some locations you can find the dynamite installed by other treasure hunters; it can be activated for emeralds.