Understanding the fundamental factors that define the flammable range of ammonia is essential for developing predictive tools to identify safe storage conditions, thereby facilitating its widespread use as an energy carrier. In this work, a numerical framework is established to predict and analyze the flammable range of ammonia and ammonia-hydrogen mixtures. To achieve this, a freely-propagating-flame method, adapted to account for radiation heat loss from nitrogen-containing species, is combined with an established ammonia oxidation mechanism, and the roles of initial temperature, pressure, and dilutant concentration are thoroughly investigated. It is found that, especially at the rich extinction limit, ammonia-related radiation plays a dominant role in causing an earlier extinction, especially at high initial temperatures. Also, the upper flammability limit is found to be particularly sensitive to third-body reactions. Incorporating ammonia collision efficiency into kinetic models is recommended as a key next step in enhancing the predictive accuracy of numerical tools.