There is no option to select all the thousands of mails from your inbox and delete it however you can increase the number of mail views in your inbox and select them all and delete them, which is faster and less time consuming than the default mail settings.
- To do so, open your yahoo mail inbox, click on the option drop down menu and select Mail Options.
- In the Mail Options, go to the General, on the Customize on how you read and send your email (Behavior)
- Select the option In The Scrolling List (Hide Preview Panel) and click on Save.
- Go back to your Yahoo mail box, now select on the check box to select all the mails in your inbox and delete them.
This steps are very similar for other email providers such as gmail, outlook mail, etc. Just go to the mail settings of those email and change the view for the number of email seen in one page and click on Save.