There comes the IFTTT, which you can use to get the functionality back, though this will require few extra step to set up.
I’m assuming you have flickr account otherwise you wouldn’t have searched for this, right? 😛
Now, get an account on IFTTT, and go to “Create” from the sidebar. You will see something like this.
Click This, and search for Email. You will see “Send IFTTT any email” when you click Email, and then click “That”. Search for Flickr, and “Upload public photo from URL”.
Don’t touch Photo URL field: It is automatically set to email’s attachments. What you type in email Subject will become the title of your flickr file, and the same happens for the description – your email body will become the description. Remember to remove email signatures from the email!
Click Create Action, and Finish. You’re done!
Now, you can email [email protected] and it will convert your email to flickr post. Note that, as this is not an official product, it may take one or two extra minutes to publish on Flickr, but it should be there anytime soon.