O.K., the coverlay and adhesive don't continue in the rigid part, but the flex substrate does. In so far your stack up looks better now. The stack up still doesn't look feasible at all. You have a polyimide soldermask defined for the rigid part which makes no sense. You should also consider that a copper layer below the polyimide substrate means to have a double side plated flex part, the bottom copper can be of course removed.
I understand now the notation of the PCB designer stackup.
Required gerber files are artwork respectively contours for all layers in the stack up. You can prepare an example set and send it to the PCB manufacturer to check if they understand it and are able to make it this way.
Some PC tools have difficulties to generate partial mask files (solder mask contains only the rigid part, coverlay the flex part), otherwise the PCB manufacturer need to separate the data.