Unfortunately, this app cannot do that.
This app uses a security-focused design that stores your diary data only on your device.
For this reason, your diary cannot be published externally, and there are no public URLs. There is no sign-up either; device transfers and backups are handled entirely through Apple's own mechanisms.
If you do want to share an entry, tap the menu button at the top right of the diary page and choose "Send a Image". Check the preview, then use the share button to save or share the image.
You can then post that image to social media or share it however you like.