A wooden bed flatpack can be made at a workbench (Wooden workbench or better) in the workshop of a player-owned house. Like when making the normal wooden bed, this requires 20 Construction, uses 3 planks, nails, 2 bolts of cloth and gives 126 experience. The flatpack can then be used on a bed 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 wooden bed flatpack from scratch gives a profit of: -4,019. This assumes the nails did not break, and steel nails (highest nail available at sawmill) were used.
After completing the hard Fremennik achievements, hey can also be traded to Advisor Ghrim in exchange for 205 coins being added to your kingdom's coffers in Miscellania. See Flatpack: Miscellania reselling for details.