Integrated sensing and communications (ISAC) systems have gained significant interest because of their ability to jointly and efficiently access, utilize, and manage the scarce electromagnetic spectrum. The co-existence approach toward ISAC focuses on the receiver processing of overlaid radar and communications signals coming from independent transmitters. A specific ISAC coexistence problem is dual-blind deconvolution (DBD), wherein the transmit signals and channels of both radar and communications are unknown to the receiver. Prior DBD works ignore the evolution of the signal model over time. In this work, we consider a dynamic DBD scenario using a linear state space model (LSSM) such that, apart from the transmit signals and channels of both systems, the LSSM parameters are also unknown. We employ a factor graph representation to model these unknown variables. We avoid the conventional matrix inversion approach to estimate the unknown variables by using an efficient expectation-maximization algorithm, where each iteration employs a Gaussian message passing over the factor graph structure. Numerical experiments demonstrate the accurate estimation of radar and communications channels, including in the presence of noise.