Frustrating! It seems the only way to delete documents is to open it so it appears in recently viewed list. Then you hold your finger on one document until the trash can appears. Then you can delete. There must be abetter way but I am unable to find it and most of the people answering in the forums don't seem to understand the questions. In other words, they are answering the question to which they do know the answer!
You need to go to the Document Cloud or Local view (not Recent). Then click the ... icon (upper right). Then click Select. Click to put checkboxes beside the names of the files to delete. Then click the Trash Can icon.
Currently, the latest version of Adobe Acrobat DC doesn't allow deleting documents from the Local file storage within the application. You will need a third party file manager(available on the Google Play Store) to do the same. However you can delete multiple Recent documents from the Reader application by long pressing a filename and then selecting multiple files you want to delete.
We regret the inconvenience caused to you and we are actively trying to bring back the functionality of deleting documents directly from the local file listing like in the earlier versions of Adobe Reader. You might see it in a future release.