This quest was designed so that you would have to choose which two of the three to save, but several exploits were found to get around that.
In addition to Pickpocket (level 2 required) you can also kill one of the cured NPCs to get a flask back for the third (with no loss of reputation).
You can also duplicate the flasks.
To copy an item; quick save the game, then drag an item out of your inventory, but not somewhere there is a red X. Without dropping first, quick load the game, then release the mouse button when it starts to load. This will produce a copy of the item on the ground, with the original still in your inventory.
There is a much easier method for items which can be stacked;
Drag a stack out of (or into) your inventory (or container) and hold down the control key before dropping. This will bring up the split stack pane; type in a negative number and hit enter (the checkmark will be greyed out). This can also be done in the trade window.
