Streaming disaster damage assessment (DDA) aims to automatically assess the damage severity of affected areas in a disaster event on the fly by leveraging the streaming imagery data about the disaster on social media. In this paper, we focus on a dynamic optimal neural architecture searching (NAS) problem in streaming DDA applications. Our goal is to dynamically determine the optimal neural network architecture that accurately estimates the damage severity for each newly-arrived image in the stream by leveraging human intelligence from the crowdsourcing systems. Our work is motivated by the observations that the neural network architectures in current DDA solutions are mainly designed by AI experts, which often leads to non-negligible costs and errors given the dynamic nature of the streaming DDA applications and the lack of real-time annotations of the massive social media data inputs. In this paper, we develop CD-NAS, a crowd-driven dynamic NAS framework that is inspired by novel techniques from AI, crowdsourcing, and estimation theory to address the dynamic optimal NAS problem. The evaluation results from a real-world streaming DDA application show that CD-NAS consistently outperforms the state-of-the-art AI and NAS baselines by achieving the highest disaster damage assessment accuracy.