This app was mentioned in 8 comments, with an average of 1.50 upvotes
I been using Turbo FTP & SFTP Client for a few months without issues. Here's a quick tutorial since it may not be completely user friendly for everyone.
-Open the app, hit Create New Account>FTP (slide from the left if you don't see this option)
-Enter a Connection Name (eg, Vita or PSTV, really anything)
-User Name and Password leave blank
-Host = whatever number is shown on VitaShell/molecularShell after ftp://(eg, 192.168.0.52 this will be displayed after pressing Select in VitaShell)
-Port = the remaining numbers after ':' (1337)
-Go to the very bottom now, leaving the other Settings the way they are and select the Default Local Folder (where you want files to save when downloading from your Vita to your phone) then hit the Save icon when done. It looks like a Floppy disk in the top right.
The free version of the app only saves one connection at a time but you can simply Edit it if you need to make a different connection. Also rooting your phone isn't necessary
Hope that helps.
Dunno about iOS, but I've been using my Android tablet ( when my PC crapped out ) to transfer .vpk's and maidumps with Turbo Client I'm sure there are alternatives, but this one worked best for me.
Since you can use Android apps on your Chromebook, I'd recommend Turbo FTP https://play.google.com/store/apps/details?id=turbo.client
Does the job, and works well on Chromebooks.
I use this to get a GUI for sftp. Has worked fine for me.
I use this one and it always works. When it tells you to put in a password just click ok https://play.google.com/store/apps/details?id=turbo.client
Is ftp/sftp an option? I'd check out Turbo if it is.
I'll update my comment if I think of anything else.
I use turbo client: https://play.google.com/store/apps/details?id=turbo.client
Not sure about anything for iOS though.