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 pop-up menu which should include Send to Kindle option.
- Choose Send to Kindle option, which will list the wrong title and author for the book. Edit title and author, checkmark the devices you wish to send it to as well as Archive in your Kindle Library, and press send.
The book didn't show up on my device immediately, but within 5 minutes it appeared in the app's home view.
I'm not sure what if any combination of events was required to get it downloaded to my device. I received an email from Amazon informing me that my document had been prepared and providing a link. I clicked that link from my phone. I also visited the store within the Kindle app. I'm not sure whether either of these acts was necessary or sufficient for finally accessing the book from my app.