I believe I figured it out, this url will clear the cart, add items with a selling_plan and then redirect to checkout:
https://{SHOP}.myshopify.com/cart/clear?return_to=/cart/add?items[][id]={VARIANT_ID}%26items[][quantity]={QUANTITY}%26items[][selling_plan]={SELLING_PLAN_ID}%26return_to=/checkout
To head to the cart page instead of directly to checkout, you can remove the %26return_to=/checkout.
Cheers,
Phil