Breeding of Leafy Sea Dragons has never occurred in captivity. This has been a goal for many professional aquarists at public aquariums around the world, and yet no luck so far. There is one person in the world that can legally collect these guys in order to sell them. He resides in Australia, and is permitted to collect one male with eggs per year. The male will give birth in his facility, and then the young will be reared and sold while the father will be released back to the wild. Their main diet is live mysis, however, you can transition them to eating a nutritious brand of frozen mysis, and even enriched live ghost shrimp. Leafies are extremely sensitive to any abrupt change. Just a sudden illumination of your lights can send them into a convulsion. They are also susceptible to uronema and mycobacterium infestations in captivity, especially if you do not keep up with vacuuming out their poop and decaying food.
So, to sum it up, Leafy Sea Dragons are expensive to purchase, if they die in transit, you will not get your money back or receive a new animal, they are extremely finicky, they need cold water and a big tank, they eat only expensive food in which they need almost a constant supply, you have to work your butt off on a daily basis to ensure they are happy, and the best aquarist is lucky to get them to live to 5 years.
If you are going to make the commitment to keeping sea dragons, you may want to research weedie sea dragons, I am not sure if they are available to the hobby, but they are typically a bit cheaper and sometimes a little hardier.