You mentioned you have set the Finder Preference. But have you selected an external disk in the Finder sidebar? Therefore, what you need to do first is to check whether you do the correct settings of your Finder. Here's how:
- Insert your flash drive into your Mac/MacBook.
- Open Finder > Settings… > Sidebar.
- Select External disks under Locations.
After that, check whether the flash drive shows up in the Finder sidebar.
And you referred to that you can see the flash drive in Disk Utility, you can use it to run First Aid and repair your flash drive.
- Open Finder > Applications > Utilities > Disk Utility.
- Choose the flash drive in the left sidebar.
- Click First Aid in the top menu.
- Select Run in the pop-up window.
If Disk Utility can detect the problem, it will be fixed automatically. After these steps, you can check if the flash drive shows up in the Finder sidebar.
If you still can't see the flash drive in the Finder sidebar, you can format the flash drive and before that, you need to back up your data.