Summarize the following:
Tap the Yahoo Mail app icon, which resembles a white envelope on a purple background. This will open your Yahoo Mail inbox if you're logged in. If you aren't logged into your account, enter your email address and password when prompted before proceeding. Doing so will prompt a checkmark to appear to the left of the email after about a second. Unfortunately, you cannot clear your entire inbox at once on mobile. Tap every email that you want to delete. A checkmark will appear to the left of each email you tap. It's a trash can-shaped icon at the bottom of the screen. The selected emails will be moved into the Trash folder. This is in the upper-left side of the screen. A pop-out menu will appear on the left side of the screen. On Android, the ☰ icon is on the left side of the search bar that's at the top of the screen. You'll find it in the middle of the pop-out menu. It's to the right of the "Trash" heading. Doing so empties the Trash folder, thus removing permanently the emails from your account.

Summary:
Open Yahoo Mail. Long-press an email. Select other emails for deletion. Tap the "Delete"  icon. Tap ☰. Scroll down to the "Trash" heading. Tap the "Trash"  icon. Tap OK when prompted.