Flying base stations, also known as aerial base stations, provide wireless connectivity to the user and utilize their aerial mobility to improve communication performance. Flying base stations depend on traditional stationary terrestrial base stations for connectivity, as stationary base stations act as the gateway to the backhaul/cloud via a wired connection. We introduce the flying base station channel capacity to build on the Shannon channel capacity, which quantifies the upper-bound limit of the rate at which information can be reliably transmitted using the communication channel regardless of the modulation and coding techniques used. The flying base station’s channel capacity assumes aerial mobility and ideal positioning for maximum channel capacity. Therefore, the channel capacity limit holds for any digital and signal processing technique used and for any location or positioning of the flying base station. Because of its inherent reliance on the stationary terrestrial base station, the flying base station channel capacity depends on the stationary base station’s parameters, such as its location and SNR performance to the user, in contrast to previous research, which focused on the link between the user and the flying base station without the stationary base station. For example, the beneficial region (where there is a positive flying base station capacity gain) depends on the stationary base station’s power and channel SNR in addition to the flying base station’s own transmission power and whether it has full duplex vs. half-duplex capability. We jointly study the mobility and the wireless communications of the flying base station to analyze its position, channel capacity, and beneficialness over the stationary terrestrial base station (capacity gain). As communication protocols and implementations for flying base stations undergo development for next-generation wireless networking, we focus on information-theoretical analyses and channel capacity to inform future research and development in flying base station networking.