There are several different types of flybacks. Most computer and terminal monitors use flybacks which have the high voltage rectifier built in. Having the rectifier built in usually isn't desired for high voltage experimenting. This is because the rectifier is only half-wave. So with a flyback with half-wave rectification (no filter cap) the voltage will only be 45 percent of the actual voltage (this is an average, the peak power remains the same) that is developed across the secondary. This doesn't apply if you use a filter cap. The CRT on modern TVs and monitors is also the high voltage capacitor. Flybacks with built in recitifers are still usable, but they are nothing like the flybacks with the old disk shaped secondary. These flybacks are more useful for high voltage experimenting since the high voltage recitifer can be removed which will allow you to work with the AC voltage. Search in tube type TVs or older solid-state TVs for these flybacks. Some of the disk shaped flybacks contain a diode too, but these are normally easy to remove with a small saw.
1. This is an older flyback. As you can see it has a disk shaped secondary. It also has a built in high voltage rectifier diode. The diode is obviously contained in the large "stick" that the black high voltage wire is connected to. As you can see I wound a primary on one side with some 21 gauge wire.
2. This is a cylindrical monochrome flyback. It has a built in high voltage rectifier. This type doesn't work too well with the flyback driver that uses two 2N3055s.
3. This is by far the best type of flyback to use for both circuits. It can make some very hot arcs and high voltages. It has no built in recitifer and has a very disk shaped secondary. The flyback pictured here is missing its core. This is because it is brand new and they don't come with the cores or primary windings. Look in old rotary tune TVs for these.
4. This is a modern color VGA monitor flyback. It was taken from a dead Compaq SVGA monitor. These are probably the worst type you could use. They have a built in rectifier, have cylindrical secondaries, and most have a focus divider on them as well.