how do i get permission to read and write to my time machine?

time machine, iOS 9.0.2

If I take this at face value it makes no sense.. Time Machine is Mac software.. nothing to do with iOS.

If I interpret what you are saying as Time Capsule.. then apple never built in file access to iOS.

Buy a file application like filebrowser and that will enable you to copy and paste files to and from the TC.

https://itunes.apple.com/au/app/filebrowser-access-files-on/id364738545?mt=8

There are a number of alternatives..

You cannot access a Time Machine backup though.. again if that is what you mean.

I guess it is hard to know precisely what you mean.. so spell it out a bit.