Flush eaves - possibly a contradiction in terms - or even the more common corbelled eaves, do not provide the "throw-off" of a 200mm box eaves and can be sources of damp ingress for this reason where gutters are in poor condition.
Normal box eaves are designed to protect the walls below by ensuring that defective gutters do not allow them to become saturated during heavy rain with consequent damage due to frost action on a wet wall leading to spalling or cracking of the surface.
Boxed eaves with outboard gutters also give timely warning of gutter problems [backfall, inadequate sizing, blockage or poor section connection/sealing] by simply dripping on your head.
Flush eaves may allow their attached - presumably equally flush - gutter to dribble down the external wall if its defective and laypersons seldom look at gutters to check for defects.
If you're after a really "clean" look you might wish to consider a hidden gutter detail also.
These can - depending on how they are detailed - removes the need for external gutters and pipes
They will bring an increased risk of damp or water ingress and more internal slab penetrations at ground floor.
But really, you should be talking to an architect or archtiectural technician for the design and/or detail of such things.
There may be other significant matters that will need to be addressed such as the support detail at the eaves.
This is not an add-on matter and would benefit from the input of a building professional at an early stage.
Archiseek might prove to be a more useful source of the technical information you require.
On that basis, I think you may be in the wrong forum.
ONQ.