SSAS -> New cube contains two fact tables. How do I relate these so I can use measures from both at the same time?
You're focusing on facts and forgetting about dimensions.

Years of service is a measurable attribute of a Driver, so, you should have a Driver dimension associated with the FactDeliveryDriver fact.

driverSid is a surrogate key for the Driver dimension, and not for the fact table. For the fact table it's a lookup column.

Also, deliveries are (probably) made by a Driver, so you should have the Driver dimension associated with the FactDeliveries fact as well.

There should also exist a Delivery dimension, that is associated with the FactDeliveries.

A simple schema should be something like:

Driver(sk_driver, name)
Delivery(sk_delivery, address, date_delivered)
FactDeliveryDriver(fk_driver, val_years_of_service)
FactDeliveries(fk_driver, fk_delivery, val_miles)


Since the Driver dimension is common to both fact tables, you can use the Driver dimension to relate measures from both of them.