Now the galleries load on mobile and IE, with the thumbnails arranged in a grid - so, I assume IE defaults to loading the non-flash based version, while in Firefox or Chrome I am still getting "Flickr Photoset Not Found" error.
No. As long as Adobe Flash Player is installed and enabled in your browser and SimpleViewer's useFlash Embed Code Parameter is set to 'true' (by selecting the 'Use Flash' checkbox in svBuilder-Pro's 'Customize -> Embed' section), the gallery should be displayed by the Flash Player rather than the Mobile Player (in IE as well as Chrome, Firefox and other browsers).
Try checking your Adobe Flash Player installation by visiting this web page in your IE browser: https://helpx.adobe.com/flash-player.html
You might find that uninstalling Adobe Flash Player and then reinstalling it will help.
Unfortunately, Flickr made a change (in September 2016) which has resulted in all Flash-based applications (not just SimpleViewer) being unable to display Flickr images. Please see this forum post for further information.
You could certainly force your galleries to be displayed by the Mobile Player on all devices and in all browsers (so that your Flickr images can still be displayed by SimpleViewer) but Juicebox would be a better option. Juicebox is an HTML 5 image viewer which does not use or rely on Adobe Flash at all. Also, Juicebox supports far more configuration options than the Mobile Player within SimpleViewer (which was designed as a fallback mechanism for non-Flash-enabled devices rather than a fully-featured image viewer itself).
To force your galleries to always use the Mobile Player, deselect the 'Use Flash' checkbox (in svBuilder-Pro's 'Customize -> Embed' section) or edit your gallery's embedding code and change the useFlash Embed Code Parameter from 'true' to 'false'.
SimpleViewer Support Team