There is generally no reason to do this. You can either use voom before running limma or run eBayes with trend=TRUE. Either of these methods should give better results than using VST data.
Yes, limma will accept vst output from DESeq. You should analyze it using the limma-trend pipeline and this should work fine. However, as Ryan has pointed out, limma doesn't require variance stabilized input and using limma's native pipelines is probably better.