Is it possible to invoke an intermediate block(voice prompt, lambda, etc.) in a contact flow(rather than starting from the beginning) when you use the transfer-to-flow feature from another contact flow?
Easiest way to achieve this (at least the one I can think of right now) would be to set a contact attribute containing a flag in the first flow, then forward it to the other flow and check wether the flag is set. If the flag is not set, start the normal contact flow. If it is set, start with your desired block.
Edit: Maybe you could also try to modularize your flows and then forward the contact to the module instead of the flow. Depends on your use case.