Right now I use FocusWriter (which is fantastic) but I need to be able to work on my phone. Just spent three weeks overseas without access to the story, because I didn't bring my laptop.
FocusWriter saves as either TXT or RTF. You could save them on, say, DropBox, or the iCloud Drive if you happen to have an Apple product, and access them from a suitable app from there. I only know iOS, so I only can recommend apps here. For a TXT file, you can use a simple text editor. There are a lot on iOS; I only have some markdown editors, but they could edit also basic TXT as well. For instance Byword (~$12). There's also a nifty app called Textedit+. Seems to cost only ~$5, but can open and save both TXT and RTF.
Scrivener has an iPhone version, with syncing. That’s what I use. (Don’t rely on the syncing as backup, however, because it...syncs! So if something goes bad, the badness propagates.)
Which is the truth for any platform that cross-syncs, so every once in a while I pull a copy out of Dropbox and pop it into my Documents folder, just in case and out of the same concern.
