Use Dynamic Delivery Price on the zip code:

1. Open the zip code entry (or select several and use Edit for bulk).
2. Click the + next to Dynamic Delivery Price.
3. Enter the Cart Subtotal at which the new rate starts (e.g. 100) and the Delivery rate (e.g. 0).
4. Save.

When the customer's subtotal is greater than or equal to the threshold, the delivery fee becomes that rate. You can add several thresholds (e.g. ≥$50 → $5, ≥$100 → $0); the highest threshold reached wins. Rows whose Cart Subtotal is 0 or empty are ignored.