Written by Kevin Wald
The text under the flags describes them in some unknown language; from this, the vocabulary and grammar of the language can be determined to a considerable extent. (Here is a dictionary and grammar for the language.)
Only one flag is not described -- the flag that has been displaced from the array of flags. It can be found further down the page, as the white box with the horizontal black bar. The description of this flag is
Nastare dryl prasu ut(That is, "on a white background, one black horizontal bar"). This description has eighteen letters; when these are entered in the eighteen numbered boxes (nth letter in box n), they spell
Since a duru is an inverted T-shape, an udyru is an inverted inverted T-shape -- that is, a right-side-up T. A starlet (small star) is a wodel (woda, "star", with the diminutive suffix). Finally, pan (7) minus sar (4) equals tas (3). Thus, in the boxes on the right we enter
PAN - SAR
which, read in order with appropriate spacing, is TWO DELTAS. A single capital-delta shape is an uta, so two of them are unte am, and the solution to this puzzle is (appropriately to the scenario described) unteam.