Prepopulate custom fields during checkout with data from user account
If I am not mistaken, you can do this with rules. Use the 'after saving a new commerce order' event and choose to 'set a property' on the commerce order. For the value you can navigate to the customer profile and select your field.

Optionally you can also add the 'after saving an existing commerce order' to update the field at every step in the process. (commerce saves the order after each checkout step).

Update

This requires some knowledge about how Drupal commerce works. An order is created as soon as you place a product in the cart. You now have a product in the cart state. As you proceed to checkout, the order state updates with every step. If you leave the checkout, the state is frozen and you could continue it at every time.

Since your rule only acts on commerce_order_insert this means the number will only be copied if you create a new cart. (proceed to checkout your current order or delete the entire order by going to the order overview.) This is why I proposed to also add the commerce_order_update event as a trigger. That should update the number at every step of the checkout process.

Also there appears to be a misconfiguration in the rule (or I misunderstood your question). If the number is on a customer profile type, you should get it from there. [ "site:current-user:field-kundnummer" ] assumes this is a field configured on the user profile. And [ "commerce-order:owner:field-kundnummer" ] is really the user if of the order owner. (Changing that might mess up everything).

I guess you should be setting [ "commerce-order:&lt;commerce-customer-profile-reference&gt;:field-kundnummer" ] instead. That would be the field on the customer profile.