Red paint becomes available at level 31, and can be found in old wooden boxes on Emerald Island. You can also get it as a reward for fulfilling a chain of requests at the Dragôn Mysterium.
Although red paint is a rare resource be sure to collect it, as you will need it to upgrade the Smelter, to complete Merchant orders, and to craft a set of colors at the Workbench.
Please check out the articles in the Resource Sites section to learn more about where to find the resources you need.