Yes, it is supported. There are also multiple ways to achieve these.
You can use the numberBatches parameter, which is a straightforward number of consecutive systems in memory to do N-dimensional FFTs on. (See section 6.3 in documentation)
You can select the higher number of dimensions and use omitDimension[i] parameter to disable the dimensions from performing the FFT on. With it, you can do the inner-most batching and have multiple types of batches with different strides. (See section 6.5 in documentation)
istride, idist and other parameters can be set with custom strides - see section 6.4
Does VkFFT support performing multiple FFTs in one call? A functionality similar to cufftPlanMany: https://docs.nvidia.com/cuda/cufft/index.html?highlight=cufftPlanMany#function-cufftplanmany