According to File Reference
You can read file directly from disc
That and many similar approaches work in the Editor … but not in the build. eg:
Globals.ProjectFolder
Globals.ProjectContentFolder
Directory.GetCurrentDirectory()
Note: there is also Globals.ProductLocalFolder, but that uses the APPDATA folder and isn’t useful for this scenario.
Yes, there is. Thanks to nuffe and Alewinn mentioning that it should work, took further steps to narrow down the issue. Now both reading from and writing to a different file is working as expected. At least with a Windows build. For other platforms, may or may not work.
Basically, it was a simple test for reading from a .txt file in the project folder.
The difference now is that originally setting up paths and file reading were done in OnEnable() of a script. Interestingly, that was working fine in the editor, but looks like some of the steps weren’t fully completed in the build it time. So moving some code to OnUpdate() when user clicks mouse button seemed to resolve the issue.
Globals.ProjectContentFolder always points to Contnet folder, you can also use file references to help with editing/usage in code: File Reference | Flax Documentation
Be sure to deploy game files with a game, manually inside .Build.cs scripts or via Build Settings: Build Settings | Flax Documentation
Great! Thank you for the direction about including files properly. That was one of the next items on the TO DO list. 
File Referencing worked for a .txt file and even for a .wav audio file that the built game was able to access.
A few follow-up questions:
Q: Using various File.Read(…) methods worked on Windows. Will that work on other platforms also to read in files that are included in the build process? What about other files that the user may place in the project folder (eg: for customizing/modding support)
Q: Oh, where can I actually find the Build Settings | Flax Documentation?
There aren’t a lot of menu options in the editor … yet missed it? Would be nice to have step-by-step instructions on that webpage.
Thanks! Will keep those in mind!
Aha! So that’s where the Build Settings are “hiding”!
I do remember opening the window … probably missed it.