This first step in this process is to make your domain the primary domain within your WordPress.com site. In order to do this the free site will need to be upgraded to a paid plan. The Personal plan will allow you to connect your domain. Once that is set you will then login to your Cloudflare account and click Add Site. When you finalize adding the site to Cloudflare you will then be given two name servers. Here is an example.
Your name servers will have different names. Now that you have your name servers you will need to add them to your purchased domain DNS settings. The next step is to log back into your Cloudflare account and in the top left click on the domain that you added. At the top, you will see many menu options. Click on DNS. The DNS page will display the records it found when you added the site to Cloudflare. You might see A records, CNAME records, and MX records if your domain is used for email. At this point, you may need to ask a technical friend to help if you do not understand DNS. In this case, our domain will only have two CNAME records.
CNAME example.com lb.wordpress.com Automatic
CNAME www lb.wordpress.com Automatic
Once those records are added your domain should now be active within Cloudflare.