Glassblower’s Baubles are used to increase the quality of a flask. Quality on recovery flasks increases the amount of life and/or mana recovered by that percentage. Utility flasks gain increased duration instead. Note that quality on flasks stacks multiplicatively with other modifiers to flasks (for example, the increased flask duration nodes from the passive tree or belts). Furthermore, things with increased flask effect will not only improve the implicit mod of a flask, but any of the mods that the flask has rolled (always rounded down).
Does Flask effectiveness increase the 2% life leech from Chaos Damage on Atziri’s Promise, the Onslaught from Silver Flask or the Increased Critical Strike Chance from Diamond Flask?
As above – yes, except for Onslaught, which is not a numerical property, but a boolean state. A character either does or does not have Onslaught, and 20% increased “having Onslaught” is still having it.
EDIT: As has been pointed out, this is incorrect regarding the Diamond flask. The question said their Diamond Flask was giving increased critical strike chance (which would be affected by this modifier), but Diamond Flasks do not increase critical strike chance, they make it Lucky, which like Onslaught, is boolean, and cannot be increased.