Are you able to expound more on what you are asking regarding promoting free shipping?
If it's about the verbiage you are after, free shipping, is what I would prefer. It clearly states that your shipping will be free in whatever context you put it in. Free plus shipping seems to indicate there is a free item plus shipping.
If I somehow misunderstood your query, apologies for the misunderstanding. I look forward to getting more info from you.
When it comes to advertising and shipping however, I have found these articles that you may find useful:
Shipping Yes FREE Plus shipping is saying a free item but the customer pays for shipping. I have been learning on using these strategies and was wondering which one is more effective in creating conversions. Thank you for your feedback I haven't been able to find someone to help on this from other websites or groups.