Congratulations, Chrome currently has the best support for local web apps. That said, these notes may help improve your experience.
Downloading files for local offline use will continue in the background while you browse the guide (including this page). However, downloading is likely to pause in any of the following cases:
If the download process is paused, just click the green button again to resume.
Chrome will prevent your screen from timing out due to inactivity while files are being downloaded for offline use, so you don’t need to actively use your device to keep the download alive.
On a computer, it is sufficient to keep the Guide tab visible (not minimized), even if another window has focus.
Chrome allows a web app to use up to 100% of the storage space available. The Guide is fairly large, but should fit easily in a reasonably modern phone.
Chrome uses a heuristic to determine whether local files are kept permanently. If the browser decides you don’t use the Guide often enough, it may delete the files if space runs short. In practice this rarely happens. If you bookmark the Guide or install it to your home screen, this will give an extra hint to Chrome that you want to keep your local files.
You can save a link to the Guide on your home screen. Open the Chrome menu and select “Add to homescreen” or “Save and Share → Install Bay Area Wildflower Guide”. On Android, this sometimes doesn’t actually put anything on your home screen. If so, you can manually drag it from Android’s installed apps to your home screen.
Because of the strange way that browsers work, every page load will attempt to fetch ~25 KB from the internet even when the site is using its local offline copy. (E.g. viewing 40 pages will fetch ~1 MB.) If you have a large or unlimited data plan, this is nothing to worry about. If you have a very limited data plan, consider putting your phone in airplane mode while using the site in offline mode.
Of course, external links will still fetch from the internet as usual. Most external links are styled and colored in the usual way for your browser (e.g. blue and underlined). Links to Jepson are in orange, and also must fetch from the internet. Placeholder boxes that link to photos at CalPhotos or Calflora are also external links. By contrast, internal links to taxons are colored brown, green, or black and use the offline copy, as do all links from a thumbnail image to the full-sized image. A few miscellaneous internal links (not to a taxon) are also in the default browser style.
Return to the Guide home and give offline mode a try.