reverse engineering camera flash charger
Its not even a chip - its a single transistor oscillator.

Here's a fairly typical circuit. Q1 (NPN BJT) forms an oscillator with T1,R1 and C1. (If you listen carefully you can usually hear its high frequency whine).
The primary of T1 is 6 turns, the output is 1750 with a feedback tapping of 15 turns. In otherwords a step up transformer. This high voltage AC is then converted to DC by D1 and used to charge up C2. After several seconds the voltage across C2 is high enough and triggers the small neon indicator (ready light). The other (trigger) coil produces a very short high voltage pulse for the flash tube causing the Xenon gas inside it to conduct and short out the capacitor - Very quickly the charge on the capacitor is used up and the flash stops.
What about the AA cell providing the energy?
The cell provides current at 1.5V. It can't supply any more than 1.5V, that's why you need the oscillator circuit to boost the voltage. The oscillator circuit draws quite a large current from the cell (that's why batteries don't last long in flash guns). As voltage is stepped UP by the transformer the current is stepped DOWN. That's why it takes several seconds to charge the capacitor.
Simply connecting an AA cell to any capacitor would only allow it to charge to (nearly) 1.5V. To charge up your microwave oven capacitor you could use it to replace C2 - in which case it might get up to about 100V.
To get to 1900V you would have to build a circuit capable of supplying that voltage.
SAFETY WARNING: High voltages and charged capacitors are quite capable of killing you, even when the circuit power has been switched off. Unless you wish to put yourself forward for the Darwin Awards (taking yourself out of the gene pool by your own stupidity) I suggest you leave hacking microwave ovens well alone.
One small slip for screwdriver, one giant blue flash for man.