I don't own a kindle or any e-ink reader though and all the Ebook apps are paginated on my iPad and Mac.
iBooks, at least, offers a scrolling option (same menu where you select font size)
interesting... most of my ebooks that I have opened in iBooks on the iPad are pdfs which don't have that option so I assumed they didn't have the scrolling option but I was able to do it with an actual ebook. It would sure be nice to have continuous scrolling on pdfs as well.
edit: iBooks on mac os doesn't have a continuous option.
Documents by Readdle is a fantastic PDF reader for your iPad. It does have a continuous scroll option as well as pagination.