I've seen this question asked on the forums before, but with no help. I hope this gets the attention of someone from the staff.
I created a discount code that should apply to everything, but the field to type in the code is not showing up. I dont have a desktop to test this, but its happening on mobile.
Ok I have identified the problem and solution on my side. I'm using an app called Dynamic Product Options which creates a draft order, and this conflicts with the default checkout process. Fortunately, in their settings they allow you to choose Default Checkout instead of Draft Order. Once I switched back to Default Checkout, the discount code field appeared again as expected.
I hope this helps someone else.
In my case I double checked my Discounts in Shopify Admin.
It turned out that I did not have any active coupons. All of my coupons were set to be active in the future.
So as part of your troubleshooting, double check the active dates (including expiration date) on your coupons. Usage limits, etc.
Because it appears that Shopify will only show the Coupon Code feature on checkout if your site has active coupons and no other restrictions set in the coupon code admin page.