I do see some Port Conflict errors inside your logs, so you could try changing your Router Mode to Localhost and then see if that works (Preferences>Advanced>RouterMode).
Additionally, your MySQL version in Local is 8.0 but on Flywheel it’s 5.7, so that could also be a problem. I know Flywheel is currently running some updates to 8.0 eventually, but for now it’s always a good idea to make sure your WP/PHP/MySQL versions line up.
Lastly, if you’re still having trouble, as a workaround the WPE/FW migration plugin works going from Local to Flywheel. Free and easy to use:
Hey @micah789 - there isn’t a simple way to do this like with WP/PHP. The easiest way is exporting the existing site and then importing the exported zip file back into Local. Once you import the site, it will prompt you for the settings you want to use. Select “Custom” and then the MySQL version and a new Local site will be created with the updated environment.