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We propose Flexible Vertical Federated Learning (Flex-VFL), a distributed machine algorithm that trains a smooth, non-convex function in a distributed system with vertically partitioned data. We consider a system with several parties that wish to collaboratively learn a global function. Each party holds a local dataset; the datasets have different features but share the same sample ID space. The parties are heterogeneous in nature: the parties' operating speeds, local model architectures, and optimizers may be different from one another and, further, they may change over time. To train a global model in such a system, Flex-VFL utilizes a form of parallel block coordinate descent, where parties train a partition of the global model via stochastic coordinate descent. We provide theoretical convergence analysis for Flex-VFL and show that the convergence rate is constrained by the party speeds and local optimizer parameters. We apply this analysis and extend our algorithm to adapt party learning rates in response to changing speeds and local optimizer parameters. Finally, we compare the convergence time of Flex-VFL against synchronous and asynchronous VFL algorithms, as well as illustrate the effectiveness of our adaptive extension.