I agree it is a little more strained, but not fundamentally. Each flag can be treated as reading out an angular direction relative to gyroscope providing reference (conceptually). The key point for me about type of geometric object is that the wind measurement of the 'wind field' requires specification of the position and states of motion (including rotation) of the collection of flags. Change these, and you have a different measurement. You cannot talk about observing the wind field without specifying information about each and every flag. Having done so, each flag's read out is, indeed, described as (say) a pair of angles (assuming it has full range of motion) in time, each of which would be computed in GR as a Lorentz scalar function.