Transfer Domain Name From Namecheap to Cloudflare

Caveats

Cloudflare doesn;t offer email forwarding service
You must use Cloudflare DNS, which is free.

NOTE: Refer Should I use Cloudflare Registrar?

Steps

Disable Auto-Renew
Switch off WhoisGuard protection: Click Manage -> Domain -> WhoIsGuard, toggle off.

Enter your site (e.g. mydomain.com)
Select a plan: Free
Review your DNS records: All DNS records will be imported automatically. Under proxy status: Orange cloud means HTTP request will go through Cloudflare (for SSL, optimization/caching, etc). Toggle it for Grey cloud to enable DNS only.
Change your nameservers: Copy DNS to be changed at Namecheap.

Go back to Namecheap, click on Domain List.

Click Manage -> Domain -> Nameservers. Change from Namecheap BasicDNS to Custom DNS. Put in both Cloudflare nameservers: usually it is adrian.ns.cloudflare.com and ken.ns.cloudflare.com. Click the Green Check/Tick icon.

Go back to Cloudflare, click Done, check nameservers. This process might be immediate or take a few hours (Cloudflare will notify you by email when the process is completed). You can try clicking Re-check now. You can proceed to Domain Registration without DNS/nameservers confirmation.

In Cloudflare, click on the Top dropdown menu and click Domain Registration.

Check the domain name and click Confirm Domains.
At the Transfer your domain from Namecheap page, follow the instructions to get Authorization code from Namecheap.

Go back to Namecheap, click on Domain List.

Click Manager -> Sharing & Transfer -> Transfer Out, click UNLOCK. Remember to disable WhoisGuard.
Click AUTH CODE, select a reason and click Send Code.
Check your email for the email from [email protected] with the subject Requested Authorization Code. Copy the Authorization Code

Go back to Cloudflare Transfer your domain from Namecheap page, key in the Authorization code and click Confirm Authorization Codes

Confirm contact information: Enter contact details (Cloudflare will redact personal details from whois query). Click Confirm and Finalize Transfer.

You will receive an email from [email protected] with the subject Domain mydomain.com transfer confirmation request which notify you when the transfer shall be completed (usually within 5-7 days). Sadly there is no way to expedite this process, so we just have to wait.

The transfer process is automatocally completed when the actually transfer happened within 5-7 days.

You have to pay $8.03 for the domain transfer/renewal which will extend the domain for one more year from the expirity date (not date of transfer). Cloudflare will automatically handle yearly renewal as well.

References:

https://developers.cloudflare.com/registrar/transfer-instructions/namecheap/