They can be replaced, but be warned you need to replace the faulty unit with one identical in spec or nastys will happen, also since they are the generator of some seriously wicked HF High Voltages (20 - 50 KV) they can flatten you before you can say snot
Often times replacements are more expensive than the screen, and usually not an option unless you happen to have another sitting around with the exact same transformer and something else wrong (ie bad tube vacuum)
http://en.wikipedia.org/wiki/Flyback_transformer