For flipbooks that don't have a direct download button, Chrome extensions can "scan" the pages and compile them into a PDF. My Flipbook Flipbook Downloader Extensions: Tools like AnyFlip to PDF Downloader
This usually only saves the currently visible page and may include browser UI elements. Important Note: Convert Anyflip To Pdf Free
If the author has enabled the "Print" option for the flipbook, this is the easiest and safest way to save it. For flipbooks that don't have a direct download