I have tried to test it, and yes, I saw what you are describing. First time I've opened your site on the android phone – it showed up the flash version. The same thing was when I installed the user-agent switcher in my computer and pretended that I am an android device.
But this is it, no matter what I've tried, I couldn't recreate it. I tried other browsers, clearing cache and cookies, it was showing me the mobile version. Have you noticed any pattern or have any ideas how can I see it again?
Do you have this issue when you open
https://www.photo.gallery/demo/x2 on your phone? Right now I suspect this is something related to your server. The fact that you're the only person reporting this indirectly supports this theory.