An experimental facility was recently developed at the Georgia Tech Research Institute to measure the acoustic scattering coefficients of a test article under mean flow, high-temperature, high-amplitude, and higher-order mode propagation conditions. The experimental facility acts like a two-sided impedance tube, in which the measurement section is a circular duct with 16 acoustic drivers and 16 microphones mounted on each side of the test article. Such a facility can be configured for grazing and bias flow measurements of acoustic liners with sound traveling in and against the direction of the flow. The new facility is designed to maximize the accuracy of acoustic measurements of higher-order modes in heated flows. The influence of experimental uncertainties on the acoustic measurements is analyzed using a Monte Carlo method. Measurements of half-wave resonators in quiescent air and heated flows demonstrate that the experimental uncertainty decreases as the absorption coefficient increases. High-sensitivity microphones produce extremely low uncertainty, and even lower-sensitivity pressure transducers are sufficiently accurate for many applications. This paper is intended to serve as a reference for designing and analyzing an experimental facility to measure the acoustic scattering coefficients in heated-flow and higher-order mode propagation conditions.