Syncing iPhone with Shotwell

As far as I'm aware, no free/open source software (including Shotwell) is capable of this. It's one of the sad facts of life that comes with using a proprietary device.

As a Shotwell developer and iPhone user, believe me, I'd love to see this. But it's unlikely to happen (barring some decision to open up on Apple's part.)

Shotwell should open automatically when the iPhone is plugged in if you have set it to manage your photos by default, however it only allows you to import photos manually and has no syncing feature AFAIK.

You can read details on how to import photos on their site here