Destruction sprees appear to be very similar in nature to massacre sprees. A great place to play around is the Cemetery of the Forsaken in Act I (blow up gravestones).
From playing around with my barbarian:
- A destruction spree starts at 6 destroyed items (unless you haven't gotten that high yet)
- The spree ends if you do not destroy something within around 1.75 seconds (I'm sure I'm a bit off)
- Even if you destroy a bunch of items at once (a cluster of urns in a crypt, for example), the 1.75 second rule seems to still hold true.
- Killing monsters seems to have no prolonging effect on the spree (I got a spree notice within ~200ms of killing a mob)
So, in order to maximize a destruction spree:
- Make sure you're within a short distance of your next target at all times
- Plan out a path that hits as many as possible!
- Single target destructibles if you need time to move between them
(the Cemetery of the Forsaken is a great location - there are large clusters of graves that you can travel between if you're fast - and you can easily grab the Grave Buster achievement at the same time)