In this paper we study the dynamical outcome in which black hole (BH) binary-single interactions lead to two successive gravitational wave (GW) mergers, a scenario we refer to as a 'double GWmerger'. The first GW merger happens during the three-body interaction through a two-body GW capture, where the second GW merger is between the BH formed in the first GW merger and the remaining bound single BH. We estimate the probability for observing both GW mergers, and for observing only the second merger that we refer to as a 'prompt second-generation (2G) merger'. We find that the probability for observing both GW mergers is only notable for co-planar interactions with low GW kicks (≲ 10¹ - 10² km s^-1), which suggests that double GW mergers can be used to probe environments facilitating such interactions. For isotropic encounters, such as the one found in globular clusters, the probability for prompt 2G mergers to form is only at the percent level, suggesting that second-generation mergers are most likely to be between BHs which have swapped partners at least once.