The loom and cloth can be crafted from the Shelter crafting menu with the following materials:
20x fibrous leaves
Craft 4x lashings and you will have 4x fibrous leaves left over to make the cloth with. Craft the loom from the Shelter section of the crafting menu (RB). Place your loom then access the crafting menu again. The cloth recipe will be available while standing near the loom and accessing your menu, you don't need to interact with the loom itself just be close to it.