A teak drawers flatpack can be made at a workbench (Steel framed bench or better) in the workshop of a player-owned house. Like when making the normal Teak drawers, this requires 51 Construction, uses 2 Teak planks, and gives 180 experience. The flatpack can then be used on a wardrobe hotspot in a Bedroom, either in building mode or not. This requires no Construction level and gives no experience.
The cost of making and selling a teak drawers flatpack from scratch gives a profit of -674 coins.
After completing the hard Fremennik achievements, they can also be traded to Advisor Ghrim in exchange for 113 coins being added to your kingdom's coffers in Miscellania. See Flatpack: Miscellania reselling for details.