Sneak attack goes off every attack a rogue makes, so yes on all blows.
To expand on that, sneak attack damage applies as long as a sneak attack condition is in place (hidden, invisible, flanking, etc.).
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The rogue's attack deals extra damage anytime her target would be denied a Dexterity bonus to AC (whether the target actually has a Dexterity bonus or not), or when the rogue flanks her target. This extra damage is 1d6 at 1st level, and increases by 1d6 every two rogue levels thereafter. Should the rogue score a critical hit with a sneak attack, this extra damage is not multiplied. Ranged attacks can count as sneak attacks only if the target is within 30 feet.
With a weapon that deals nonlethal damage (like a sap, whip, or an unarmed strike), a rogue can make a sneak attack that deals nonlethal damage instead of lethal damage. She cannot use a weapon that deals lethal damage to deal nonlethal damage in a sneak attack, not even with the usual –4 penalty.
The rogue must be able to see the target well enough to pick out a vital spot and must be able to reach such a spot. A rogue cannot sneak attack while striking a creature with concealment.
At 8th level, the monk can make two additional attacks when he uses flurry of blows, as if using Improved Two-Weapon Fighting (even if the monk does not meet the prerequisites for the feat).
At 15th level, the monk can make three additional attacks using flurry of blows, as if using Greater Two-Weapon Fighting (even if the monk does not meet the prerequisites for the feat).
A monk applies his full Strength bonus to his damage rolls for all successful attacks made with flurry of blows, whether the attacks are made with an off-hand or with a weapon wielded in both hands. A monk may substitute disarm, sunder, and trip combat maneuvers for unarmed attacks as part of a flurry of blows. A monk cannot use any weapon other than an unarmed strike or a special monk weapon as part of a flurry of blows. A monk with natural weapons cannot use such weapons as part of a flurry of blows, nor can he make natural attacks in addition to his flurry of blows attacks.
So as far as I can tell as long as a sneak attack is allowed it can and does affect every attack up to and including two weapon fighting and flurry of blows. Just keep in mind a Flurry is now a full round action. This may at times affect how this would work.
That would make a monk/rogue a very powerful build.
It is a non-terrible but not necessarily powerful build.
Also keep in mind that in some cases, only your first attack would be sneak attack, such as when using regular invisibility. After the first attack, they can see you and defend themselves against you.
Since flurry is essentially two-weapons fighting, that doesn't make much difference with a regular two-weapons fighting rogue.
Except that your BAB is equal to your monk level, and your SA dices are still limited by your rogue level, so either you can't land a hit either you don't add more than 1-2d6.
There's a 3.5 feat, ascetic rogue I think, that has two different descriptions, and one lets you stack rogue and monk levels for your sneak attack progression. That would make it a very powerful build, but you'd have to pay your DM.
You must be brand new to Pathfinder/D&D 3e and message boards where said games are discussed. I think the sneak attack question is older than the sneak attack ability itself. :D
There's a 3.5 feat, ascetic rogue I think, that has two different descriptions, and one lets you stack rogue and monk levels for your sneak attack progression.
The only description I found is from the Complete Adventurer, and the levels didn't stack for Sneak Attack ("only" unarmed damage). Can you tell us what is the other source you mentioned?