Baker Creek Heirloom Seeds occasionally has fibre flax available. Perhaps if more people start requesting it, they will bring it back as a regular item.
They also carry a few other heritage varieties of flax that look promising for fibre production. Just because they don't say these are for making linen, doesn't mean they can't be used for it. All flax has fibre hidden in its stem, perhaps it just needs the right conditions to make it useable. So far, I've had the best luck with their perennial flax.
Richters Herbs also has fibre flax from time to time.
At the moment of writing, they have Evelin Fibre flax in stock, but Regina Fibre Flax is out of stock. They also have a listing called 'flax' which may also be useful for fibre making. I can't tell how tall it is from the description, but if one had the room, it would be worth trying.
Wild Fibres UK also has flaxseed, however, I don't know if they ship overseas or not.
Flax for Sale is a place in the US that sells seeds as well as fibre for spinning. They don't mention if they ship internationally.
Woolgatherers sells Marilyn Flax seed which originates from Holland.
Know of any other sources of flaxseed? Please let us know in the comments section.