If the author has enabled the "Print" option for the flipbook, this is the easiest and safest way to save it.
The pros of using desktop software are that you have more control over the conversion process, and the output PDF files are usually of high quality. However, the cons are that you need to install software on your computer, and some software may require a paid subscription.
If the flipbook is protected and online downloaders aren't working, you can manually capture the pages.
Maya just smiled, sipped her coffee, and whispered, "Network tab."