Only a few fiber supplements are synthetic. Most are simply-processed agricultural products that have been in the human food supply from time immemorial. These include vegetable gums, pectins, seeds and brans. They have been studied in many species, including humans, and shown to be both safe and quite effective. A few types of fiber, the celluloses, are made from non-food plants, and one, chitosan, is synthesized from shellfish.
Psyllium seed contains a mixture of soluble and insoluble fiber.
Flax seed has a mix of fiber too. However, psyllium's soluble fiber is not fermentable, which means it doesn't feed your intestinal flora, with all the associated comfort and health benefits. It is not clear whether the soluble fiber in flax is fermentable. It might be a good idea to add some fermentable fiber too. There are many different types of fiber, but they all bind water.