I had no problem digging this out of the depths of my 'bucket with Unity as a substitute for Flash. I think I posted the link to an article with the best substitutes for flash on the first or second page.
Actually, I have had no trouble at all so far with Photobucket, without Flash or any substitute.
I can post pictures (including drag and drop) and find and retrieve links to post, which is pretty much all I do there. I suspect that is because their ads seem to work all too well without flash. It's the ads there that control the experience, as they always have priority over allowing work with pictures.
And it doesn't even nudge me to install Flash.
edit. I should probably clarify that I didn't see any new
problems with Photobucket after uninstalling Flash and not replacing it with anything else. But it may well be that I simply don't use the parts that need flash.
Photobucket still has a lot of problems, but I have a decade's worth of content stored there. And one can still load a picture, grab a link and display it here in less than a minute (assuming one doesn't try to do it in prime time).