Excellent Idea! (MAYBE there's a loophole)
First of all, I'm impressed by this strategy! It's a great idea, and turns the tables on the Beholder extremely well. You might have some trouble targeting the Beholder from within the cloud yourself, but characters normally know where other creatures are during combat (the fact that the Beholder hovers may complicate this, but probably not unless the Beholder takes the Hide action).
There is a small potential loophole I noticed, but it's not ironclad (more open to interpretation).
Legendary Action & Lair Actions
The Beholder can use its eye rays with its Action during its turn, but must choose targets it can see. However, it can also use its eye rays in two other ways: one is with a Legendary action at the end of another creature's turn. This legendary action is described as follows:
Eye Ray. The beholder uses one random eye ray.
It can also use lair actions, one of which is the following (MM, p. 27, bold added):
Walls within 120 feet of the beholder sprout grasping appendages until initiative count 20 on the round after next. Each creature of the beholder's choice that starts its turn within 10 feet of such a wall must succeed on a DC 15 Dexterity saving throw or be grappled.
Note that neither of these descriptions requires the Beholder to see its chosen targets.
It's likely that the definition of the eye rays given in the Actions section of its description is meant to apply to the other (Legendary) rays as well. But this is ambiguously worded, and open to interpretation. Clearly, some parts of the description of the eye rays must apply (or else there would be no limit to the range of these Eye Rays, for example): exactly how much applies, though, is ultimately up to the DM.
Even if its lair and Legendary actions do not require sight, note that your strategy would pretty much halve the amount of opportunities that the Beholder has to target creatures directly (as opposed to lifting a heavy object above a character while they are in the Antimagic Cone, and dropping it). This makes this strategy an excellent idea in any case.
It stays in the flask
A related question:
What happens to a bag of holding in an Antimagic Field?
The iron flask seems to function like a pocket dimension for the captured creature, which is why I'd personally rule that the flask simply turns into a normal flask, and is cut off from the pocket dimension for the duration.
The Antimagic Field spell itself seems to confirm this (emphasis mine):
Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the sphere and can't protrude into it. A slot expended to cast a suppressed spell is consumed. While an effect is suppressed, it doesn't function, but the time it spends suppressed counts against its duration.
The word suppressed is not the same as dispelled. This means its effects simply cannot be used, not that the effects disappear. This is especially true if you look at the last sentence, which specifically states that any spell cast is "active", it just doesn't do anything.
Best Answer
It's Not as Much Fun as It Should Be
The range of the 9th-level Sor/Wiz spell time stop [trans] (PH 294) is personal. The 6th-level Sor/Wiz spell anti-magic field [abjur] (PH 200) says that "it prevents the functioning of any magic items or spells within its confines." Emphasis mine.
Thus the spell time stop is suppressed until the duration of the spell anti-magic field expires.