In this case, the brick-layout will not look the way as in the picture. Each course has a different perimeter length, meaning the mortar joints will overtake each other. For this, panelling tools will be useful. But I think you need to decide on a plan of attack.
I see you have been couselled alot here in this previous thread: Mesh Panelization: Converting Curved Panels into Rectangular Elements - #23 by jessesn … I would start from the shape of a cone. This significantly simplifies things! Then you can Flow the shape flat, and consider what you will do.