A wooden chair flatpack can be made at a workbench (wooden workbench or better) in the workshop of a player-owned house. This requires 8 Construction, uses 3 planks and 3 nails, and gives 96 experience. The flatpack can then be used on the chair space hotspot in the Parlour, while building mode. This requires no Construction level and gives no experience.
The cost of making and selling a wooden chair flatpack from scratch gives a profit of: -2,486. This assumes the nails did not break, and steel nails (highest nail available at sawmill) were used.
After completing the hard Fremennik achievements, they can also be traded to Advisor Ghrim in exchange for 59 coins being added to your kingdom's coffers in Miscellania. See Flatpack: Miscellania reselling for details.