Can I change the DNS of my website URL hosted by GoDaddy to use an email address created with cloudflare, while keeping my old email address also hosted with GoDaddy? Or does changing the DNS records mean I’m loosing my first email address I created with GoDaddy?
Welcome to the Cloudflare Community. 
Cloudflare does not provide email. Cloudflare Email routing is a forwarding-only service that is used with a mailbox in another domain. You won’t be able to use it to create domain email addresses when you have domain mailboxes on another server.
Forwarding tends to be an inferior solution. If you already have domain email service with a mailbox provider, you will be better of using it and avoiding Cloudflare Email Routing.
I’m not sure if I understand.
I have a URL with GoDaddy.
Then I have an email address connected to that URL with GoDaddy.
Now, I like to create an additional email address with Cloudflare and connect it to Gmail.
Is that possible?
Thank you.
No.
You can either use your mailbox email at GoDaddy or you you can use Cloudflare Email Routing to forward incoming mail to a mailbox in a different domain. You cannot do both.
So even when these are two different email addresses?
I guess that means it is about the website URL, right?
Any emails connected to one URL can just have one single mailbox, do I understand that right?
Ok, then I will transfer my current email address with GoDaddy to Cloudflare, that’s possible, right?
No. A URL is not the same thing as a domain name and has nothing to do with your email.
You really don’t want to do that. No good will come of it. If you already have service with a mailbox provider, it is always best to use them.
You seem really determined to use Cloudflare Email Routing, despite it being a horrible idea in your situation. Can you explain your fixation with it when you already have a superior option available?
My current email will expire in 10 days and I’m looking for a free-of-cost solution. I would need to renew the subscription which cost $135 for a year. So I’m looking for a better solution. GoDaddy’s pricing is not transparent at all so I feel tricked by them into a subscription I didn’t want. I’m using Google Suite for a lot of my workflow so I thought it would make sense to connect my email to Cloudflare and then to Gmail.
Thank you for sharing those details. It is quite helpful. If you have a paid Google Workspace account, that will be a great domain email solution and can be configured without using Cloudflare email routing. See the following for how to add another domain to your Google Workspace.
I don’t have a Google Workspace paid account. Not yet. I will purchase that for my soon-to-be new business.
As a designer I have an (old) portfolio website and I like to keep that website and email address connected to it on a low budget.
Oh, I see I just watched the video. So, I could sign up for a paid Google Workspace connect my business domain (I already have) and create a business email, while I also can add another domain (the current portfolio) and switch the current email to that same workspace and that would be free. I mean the additional email would be free.
Is that right?
As long as you configure it as an alias on the same Google Workspace mailbox, yes.