Flush doors can be painted using the same system as for wall areas. Note that if you decide to use a roller for speed, the finish will be less smooth than using a brush because the roller leaves a slight orange peel effect. This may be overcome by laying-off each section with a brush once it has been rollered, as you work, but will require some practice.
The sequence for this is very important if a good finish is to be achieved. Lay off each piece along its longest dimension.
Start by painting the mouldings, taking care not to overload them as this will lead to runs.
Next, paint the panels themselves.
Then the edge of the door.
Follow this by the vertical pieces between the top panels.
Then paint the cross rail at the top, the top half of both stiles, the vertical section between the bottom panels, the lock rail, then the bottom rail.
Finally, paint the bottom half of the outer vertical pieces.
Take care to blend the joins between sections.
You will need to work reasonably quickly to get good results.
Experienced painters adopt different techniques but these rely on skill and speed which can only develop with practice. They often paint a panelled door in a very similar way to a flush door.