Why is that high voltage AC is more commonly found than High voltage DC? Example my battery powered fly swatter and fluorescent lamp both use high voltage AC. Why can't these devices increase the DC voltage from battery and directly use the High voltage DC?
All it takes to make high voltage AC is low voltage AC and a transformer.
To make high voltage DC, you have to chop it into (what else) AC, run it through a transformer, and then rectify it back to DC. Quite a bit more hardware is necessary.
So, with mass produced products, there's a strong economic bias to use AC high voltage, so that's what you'll see, unless there's a compelling reason that the high voltage needs to be DC.
Another reason for high voltage AC has to do with arcing. If an arc is formed with DC, it's very difficult to extinguish it (you need to disconnect the power source until the air gap de-ionizes).
In the case of AC, the arc is extinguished in each cycle. Once your fly is fried, you are not left with a continuous arc.
The changing current in AC makes it possible to step up and down voltages. DC to DC converters usually generate some form of AC to do the conversion most efficiently with a switching circuit of some type.
If the device can function on AC, then there is no reason to have the performance losses of converting back to DC after stepping up the voltage.
This is also why power distribution is via AC. The voltage can be stepped up to a very high voltage, which makes the current drop for the same power. This allows power to be supplied with less losses due to the resistance of the wire. Then it is progressively stepped down until it gets to the 220-240 that most homes are fed (to be used as both 110 and 220 in the US and usually 220 only else where.)