There are multiple ways to find a LinkedIn username using OSINT techniques, but most of the techniques are manual and not at all convenient to use when gathering intel. They are also not at all scalable in any meaningful way, you can't mine data for a thousand a people at once, even if you know how to grep the data. Or can you?
Never Send A Human To Do A Machine's Job
I wrote a tool to find Linkedin usernames using email addresses, using my tool you are able to retrieve the Linkedin user profile URL by inputting their email address.
Once you get the tool from Github, make sure that you provide your Linkedin username and password as mentioned in the below image in the python file.
Then execute the python file with target email address as an argument and you will get the profile url of the target email address like in the image below.
Happy OSINT gathering!