Go to Accounts and Import, then in the Send mail as: section click Add another email address that you own. A window titled Gmail - Add another email address that you own should pop up.
Enter your name and your FreeBSD email alias like yourFreebsdUsername@FreeBSD.org.
Make sure that Treat as an alias. is checked. Proceed.
Now fill in the information as follows:
SMTP Server: smtp.gmail.com
Port: 587
Username: yourGmailUsername@gmail.com
Password: The one time password you've generated a couple of steps earlier that should be in your clipboard now.
Check Secured connection using TLS (recommended)
Click Add Account.
You should receive an email with a confirmation that you want to allow Gmail to use your FreeBSD alias. The email should contain both a special code or a link to click. The easiest way is to just click the provided link so that your decision is approved.
Cheers! You should be able to send emails using your @FreeBSD address with Gmail.