Tenderize the conch to 1/8-inch thickness, using a meat mallet.
Place the conch in a pot of water. The water should just cover the conch. Boil for 20-30 minutes.
In a large pot, add the oil and allow to heat up for a minute.
Add the flour and stir to make a roux. Let the roux simmer for about 5 minutes. Don't let the roux burn!
Add the tomatoes, onions, thyme, pepper sauce/red pepper flakes, salt and pepper. Stir and let simmer for a minute or two.
Add the potatoes, tomato paste. Stir and let simmer for about 15 minutes.
Meanwhile, take the conch out of the water and cut it into small chunks.
Add the water, conch and the juice of 1 lime to the large pot.
Cover the pot and simmer until the potatoes are done, about 30 minutes.
Taste and add more salt and pepper if necessary.