anyone know if we can add custom fields to Ship Items?

To the Shipping Item record directly, no. It would be an Other Record Field, and that doesn't allow me to select Shipping Item in the setup. If it's absolutely essential that a USER see a custom field with a value on a Shipping Item, you can deploy a User Event against Shipping Items. So you could potentially use a beforeLoad to add a field and a before/afterSubmit to get that field's value, then store it in an associated custom record. Getting that value in other places like a search or a transaction form, etc. would take more work as well.

My use case would be hoping to add a custom field as a way to flag certain shipping items as special, then use that flag to support searching for "special" shipping items.

Correct. I think you'd have to create a custom record for the purpose. Single List/Record field with Shipping Method as the source. Then search on that record. You could extend that by creating also a transaction body field which you could set by field sourcing to match the shipping method selected on the order. But if all you need to do is see a list of 'special' shipping methods, you could always just define the specific methods as a filter in the search. Would need to be updated each time a shipping method is added/removed from that group, but it'd work.

If 'shipping items' are still 'items' wonder why they don't support custom item fields. Would have been convenient.

Yeah... kinda like tax items. They're items, but they're not really items.