You can get paint from the Paint Factory, which can be found in the third tab of the Store window (tap the icon with a mallet in the lower part of the screen to open it). Please, pay attention to the fact that the Paint Factory becomes available to you only at high game levels and after upgrading the main building to level 12.
If you want to get this rare resource immediately, there is no need to wait so long: you can find paint in the next-to-last tab of the Store window.