How do you get thread or yarn?

This is a multi step answer. 1st you have to build a toy car. You get wheels from chests. Toy cars give you light bulbs, use the bulbs to make post lights. When you have a LVL 6 post light a greyed out clock will appear. Once the clocks’ timer has counted down a moth will automatically spawn. Once you’ve merged moths to LVL 6 it will turn white again with a clock countdown. When the lightning bolt appears click on the moth and cocoons will spill out combine these to begin the yarn merge tree (made up of 11 segments).

No. You get it from merging the cocoons.

You can get thread or yarn via moths. The moths you get from tapping a silkworm cocoon after you have left it long enough for it to have an energy symbol form on top of it. Just tap it when you see the energy symbol.

Then you merge the moths to level 6, and then you'll be able to get silk, and then thread and yarn.