If there’s no flow title, why should the flow number “1.” have to remain (unable to erase)?
In Layout Options, I have selected Show Flow Headings: “never”
At some time you edited the text frame. This created an override. Once overridden, that option no longer has any effect. This reveals a gotcha in Elements. You need Engrave mode to reset the override.
If you can, post the project, or send it to Daniel so he can reset it.
Ah okay, thanks. Just to be sure I understand. If never type anything into the “title” block of the flow, then it won’t supply the “1.”?
And is this project by project? If I open a new project from a Dorico template should be fine. But, say, I “save as” the current project under a different name, it will propagate, right?
Hey, I just noticed something. It resets the next time you open the project! The “1.” is gone now, yay!
False happiness 
the “1.” vanished only in some of the parts, not all. Weird.
There is a work-around: propagate properties from a part that doesn’t have the “1.”
If you never modify the text frame, no override will happen. It appears you deleted the Flow name token but not the Flow number token.
You can delete a Layout and create a new one. The new one will not have any overrides since they are per layout.
Thanks Craig F. I finally figured out I can double click the token and edit it or erase it!
If you’re using Elements, you’ll find it much more efficient and easy in the long-run to change information like project titles in the Project Info dialog. This avoids page overrides, and also means you don’t have to make manual changes on every page in every layout. To remove the “1. Flow 1” title below the main project title on the first page, don’t edit it directly - hide flow headings instead. (Editing flow headings/project titles directly on the page causes a page override as other users have mentioned, which in Elements you can’t remove later because that’s only possible in Engrave mode in Dorico Pro.)
For projects where you only have a single flow, you might notice the 2nd page onwards in part layouts shows “Flow 1” at the top of the page - this is because the default master page includes a token that refers to the Flow title in Project Info. If you make the flow title the same as the project title (in projects with one flow only), this updates automatically on every relevant page.