A shaving stand flatpack can be made at a workbench (Oak workbench or better) in the workshop of a player-owned house. Like when making the normal Shaving stand, this requires 21 Construction, uses 1 plank, 1 nail, 1 molten glass and gives 30 experience. The flatpack can then be used on a dresser 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 shaving stand flatpack from scratch gives a profit of: -561. This assumes the nails did not break, and steel nails (highest nail available at sawmill) were used.
After completing the hard Fremennik Tasks, hey can also be traded to Advisor Ghrim in exchange for 20 coins being added to your kingdom's coffers in Miscellania. See Flatpack: Miscellania reselling for details.