How to terminate cooker hood ducting
Trouble is, the air is laden with moisture and will billow up around the outlet (whatever you use). This might cause staining, and even eventual rot. 

Some of the roof tile vents are very neat and small these days (making assumptions here re. your tile type!) and run the pipe up to that? Best long term option.

Also, I'd try to run an insulated pipe (or surround the flat pipe with fiberglass) between the ceiling and the vent. Otherwise the hot air can condense on the sides of the cold pipe in the attic and run back. 

If you must fit a plastic vent terminal, make sure it's well sealed to the eaves material to stop moisture laden air getting back into the attic (difficult if there are strip vents for the attic in the soffit or fascia board). 

You could consider fitting the vent into a square of metal or plastic to protect the eaves material. I've used white perspex for this in the past. 

Update
In light of the better photos and your note about being willing to drill a hole. I'll amend my advice. Go for the core drill. It's always preferable to installing in the eaves or the roof for future maintenance reasons. Plus it's usually the shortest distance from the unit to the vent which is best.

Plus, a vent in a plastic pipe fitted through a solid wall is virtually maintenance free by comparison. 

You're unlikely to run into a problem drilling a core hole through old brickwork. You'll need to hire a large special drill and corresponding core bit for best results. You can chain stitch a hole using a regular SDS drill bit and then chop out the core but this is likely to damage the wall and/or plasterwork internally. 

Core drills form extremely neat holes. But you must have a stable platform to drill from. The drills are large and the large size of the core bit means you need to be able to hold the drill very securely as they can snatch a little, especially if you're not holding it properly.

Pick up your vent parts first, especially the plastic 'drain' pipe which will go through the wall. Core bits come in various close sizes; 100mm 115mm 127mm etc. etc.