Spiking Neural Networks (SNNs) are a promising alternative to conventional Artificial Neural Networks (ANNs) due to their biological interpretability and capability to exploit sparse computation. Specialized hardware for SNNs has potential advantages over general-purpose devices in terms of power and performance. However, the computational requirements of modern Spiking Convolutional Neural Networks (SCNNs) renders most SNN hardware inefficient for SCNN acceleration. As a step towards efficient SCNN acceleration, we present IncineRate, a flexible FPGA-based SCNN accelerator architecture. IncineRate has built-in support for many SCNNs, such as AlexNet, VGG16, and ResNets, and can be extended to support other network models. The number of simulation time steps, the network architecture, and other settings are specified at run time, so an already deployed device can execute multiple networks without reconfiguration. Our results show that IncineRate achieves state-of-the-art classification accuracy among FPGA-based SCNNs on CIFAR10 and CIFAR100.