I think even the twisted surface before doing the flow already has hyperbolic parabaloid double curvature, meaning it isn't a developable surface even before the flow.

To be a developable surface it has to have one principal curvature direction as a line. Having an isoparm curve as a line doesn't do it.

If it isn't developable even before the flow then it certainly isn't going to become developable after the flow.

For example here are principal curvatures of one piece:



- Michael