Flexible syns are a device given to us to allow us to cope when we truly will not have either much control over the day or for a special occassion. As allie said - the idea is that you work out before how many syns that you are likely to need that day and try to stick with that number - be it 20/30/50/whatever.
There is no promise of a weight loss that week, but what it should do, providing you've been in control of the syns on the flexisyns day is give you the ability to get straight back on plan properly the next day.
The key is though that you are meant to keep some sort of control over the food by sticking to the syn value you have picked. Flexisyn are also meant to be used sparingly when there is little other choice. In 18 months - i've flexisynn'ed probably about 3 or 4 occassions (including an entire weekend).
First time was for brother's wedding last year (BBQ day before, wedding day, hotel breakfast and bbq day after) - i planned where i could, took control where i could, and flexisyned the rest. Went ot my next weigh-in and lost 2.5lb. Last time was when i went down to London for the an award ceremony (and a take-away treat that evening), back on plan the next day but gained half a pound at weigh-in (i don't usually drink and i normally avoid deserts these days).