All tea leaves have some fluoride in. It is a natural feature of the tea plant to take up fluoride from the soil and water. The amount in the plant depends on the concentration of fluoride in the soils as this varies between different areas of the world, industrial pollution can add to this. Organic teas would be no different in this respect.
The amount of fluoride is tea leaves increases as the leaves mature and age. This is why brick tea made from the oldest leaves of the plant contain the highest levels and cause problems of fluoridosis in places such as Tibet where the tea is regularly drunk. For this reason black tea usually has more fluoride than unfermented green teas as green teas often use younger leaves.
In fact generally the better quality green teas, particularly whole loose leaf tea, will come from the newly growing leaves at the tip of the plant. The rarest form known as white tea is produced from the young growing buds of the plant.
Cheaper tea used in tea bags and the crap tea leaves that go into instant tea comes from older leaves. Apparently heavy long-term consumption of instant tea can cause skeletal fluorosis in rare cases.
The form of fluoride naturally occuring in tea is calcium fluoride while sodium fluoride is what is usually added to drinking water and toothpaste. Calcium fluoride is less soluble in water and seems to be considered less toxic for this reason. In many parts of the world natural levels of fluoride equal that of fluoridated drinking water in the USA.
The longer you brew your tea for the more fluoride will come out of the tea. I don't see any way to get fluoride free tea. I have read many scare stories about fluoride on the internet, most people who write about it are so entrenched in the belief that fluoride is the root of all evil it is hard to get any straight unbiased facts about it. I expect worrying about it too much will do you more harm than the fluoride will.
I am also a complete tea snob and love my loose leaf teas from china. Buy some decent quality loose leaf like this and enjoy real tea in moderation. Not drinking fluoridated water or toothpaste I personally don't see this as something to worry to much about.