Assessing the similarity between an actual signal from a mid-infrared (IR) flare and the signal emission of a flame from an aircraft requires exact knowledge of the theoretical modeling of the flare's spectrum. In this study, we model the spectrum of an IR flare by considering line-by-line modeling and measurement conditions. First, we calculate the parameters of the spectral lines of a mid-IR flare using the high-temperature molecular spectroscopic database (HITEMP) and the chemical parameters of the IR flare with the combustion model in the thermodynamic equilibrium condition. To calculate the exact spectral line shape function, we introduce spectral line broadening for each spectral line in the IR flare. We also introduce the instrument function of the spectrometer to calculate the measured spectrum of the IR flare. In consideration of realistic measurement environments, we calculate the atmospheric transmission with varying altitudes, measurement angles, and humidity, and obtain the spectra of the IR flare in those conditions. To verify the spectrum model, we confirm that the calculated spectrum is in good agreement with experimental data for the IR flare.