Sure,
tobacco plants grow just fine in Florida. They make wonderful ornamental garden plants, where their flowers are noted for attracting hummingbirds. Bugs also don't chomp on them much -- after all, they grow their own insecticide! In fact,
tobacco plants can grow in every state except maybe Alaska. You start the seeds in flats, then transplant to the ground when they get large enough. Once you harvest the leaves (use gloves and a long-sleeved shirt), it's best to cure them (a garage), then you can chop them and extract the nicotine after they've cured. From planting to extracting takes about a year to 15 months.
There are many varietals available. For maximum nicotine extraction from the Nicotiana tobaccum species, burley has a slightly higher concentration of Vitamin N. I'd stay away from the Nicotiana rustica species as it's awfully high in nicotine (up to about 10% of the leaf is nicotine!) and handling the leaves can cause problems without suitable protection.
Google "tobacco growing" and similar. You'll find a ton of information. You can also find lots of different varietals in seed form available online.
To extract the nicotine, try google. From what I've read, the extraction process leaves you with "dirty" nicquid -- other chemicals get extracted, and the nicquid is prone to oxidize easily. It will be somewhat "dirtier" than Chinese-made nicquid, but it will be usable. You also need a bunch of expensive glassware and lab stuff. It's a lot easier to buy the best nicquid you can find, then freeze it in a top-loading freezer.
Just enjoy the plants!