I figured out one fairly unsatisfactory way to do it:
Using phone browser (Chrome), go to Gutenberg mobile site.
Find book (for example) and download Kindle version.
Go to Downloads (under Apps) where you should find the mobi file listed (e.g. pg174.mobi).
Long touch the file until menu bar appears at top with Share icon.
Click Share Icon which will present ...
If you are wondering where to put those .mobi files (or perhaps any other files that your android kindle app can read) if your Kindle app is located in the external storage (external sd - card), just put them at:
x: is a 28 characters long string that will be different for each user
As of 2018, Kindle did not recognise epub. So I used a web site to convert it to a mobi. But it still did not recognise it. I remembered that apps now needs runtime permissions to access the virtual SD card. So, it the app properties, I gave it the storage permission, and restarted Kindle. Now, it worked.