A great many webpages have Flash adverts, so if you're browsing news sites, etc, normal sites that people do browse, you will probably end up being served Flash and so your battery will drain.
Again: not a single one of these adverts will load when you visit your website. You will see grey boxes with an icon on Android, similar to what you see on iOS. There is no flash running that could drain battery.
On-demand flash support means that you can touch one of these grey boxes, and only then will flash load and execute the application.
On-demand flash support means that you can touch one of these grey boxes, and only then will flash load and execute the application.