Once a user is past the cart step and into the checkout itself, themes no longer have any effect on your customer's experience. You are redirected to Shopify's checkout pages that are separate from your theme.
We sometimes we get reports of discounts field not appearing in the checkout.
Most of the time, your checkout discount area looks like one of these two photos:
Shop Pay Checkout
Here's the catch: the discount code area will appear only if the products in your cart are eligible for a discount. If they aren't, that field is hidden.
So no worries, your theme isn't hiding the discount button, it's just that the products in your cart aren't able to have one applied.
As always, any issues with the checkout pages should best be directed to a Shopify Support Advisor.