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:

1. Go to Shopify Settings > Checkout
2. Either create a new custom checkout, or customize an existing one
3. On the bottom left sidebar, click "Add App Block"
4. Click "Auto apply tiers codes module"
5. Move the module to whichever part of the checkout page you want
6. Click save + publish!