The default checkout from the "send invoice" button does not allow customer to input discount code, but with Draft Helper app, you can create a separate checkout from the draft order, and you can set a discount code on the checkout, or let customer to input it on the checkout. You can then send the link of this checkout to your customer.
You can install the app (Draft Helper) here : https://apps.shopify.com/draft-helper , there's a free plan which you can try it out.
After installing the app, go to your draft order, click "More actions" on top right > "Generate discountable checkout link" , then you can send this checkout link to your customer, so that they can apply discount code.
Hope this can help!