Were the Zen Patriarchs reborn? Was e.g. the 6th patriarch Huineng reborn? Was Dogen reborn?

I would think that Huineng wasn't (it's called the platform sutra for a reason) and Dogen was - though I don't know of anything he said to that effect
There are two implications to the question you ask:

If you imply that being reborn so that they can come back to earth to teach again like the Tibetan lamas, the answer is no. That is the path of a bodhisattva. The zen tradition is to gain enlightenment, instantly or gradually.

The second is that, have those patriarch reached enlightenment so that they will never be reborn? If you believe they were enlightened then they will not.