You can auto apply reward tier discount codes + free shipping codes at checkout using the Auto apply tiers codes module. Here's how to put it on the checkout page:
- Go to Shopify Settings > Checkout
- Either create a new custom checkout, or customize an existing one
- On the bottom left sidebar, click "Add App Block"
- Click "Auto apply tiers codes module"
- Move the module to whichever part of the checkout page you want
- Click save + publish!
To view visually: