First off, lets clear how these things work. They use EMS (Electrical Muscle Stimulation) to contract your muscles.
I quote from an article that talked to a physiologist.
"These devices tend to only activate the surface of the muscle," Swoap says. The electricity causes tingly-feeling contractions around your middle, but it doesn't reach deep. To entirely activate the abdominal muscles, "You would either need to have a massive voltage from the surface (burning skin, anyone?) or surgically implanted electrodes."
These belts effectively don't train your muscles, they don't even help you burn a noticeable amount of calories.
There is a full answer on Skeptics.SE, I will only quote a part.
The results showed no significant changes in weight, percent body fat, girth or strength of the treatment areas.
The EMS device did not work for any of the claims.
Note that the question on Skeptics confused "TENS" (Transcutaneous electrical nerve stimulation) with "EMS". EMS is a a variation of TENS but serves another purpose. Both have their purpose in therapeutic applications (see @BackInShapeBuddy's comment), but not for the claims which are used to market the Slendertone belt.
And lastly, there is always the spot reduction myth. Your body will not burn fat on based on the muscles you train but in places where it prefers to take fat from and this happens to be defined by your genetics. Although some recent research suggest that there is a slight spot reduction this effect is minimal.