If you are logging stuff, it is a lot easier to simply send a message to your server and have it do the logging on the server side. That way you don't need to deal with individual timestamps from each roku device in different regions, and use your timestamp on the server for a more legible report. Typically, to do this you would only need to "AddParam" the action, a filename or video title, and an identifier for the specific roku and let the server do the rest.
If you insist on doing local end user based logging, remember you have 16KB to store in the registry for your dev key - to conserve that you'll need to wipe the log or entry and rewrite/update it before it fills up, and track your byte arrays to ensure it isn't overflowing or failing on writes. To do that you might want to consider simply saving the unix timestamp and converting it back to readable text on display, or save the date and sequence in the queue while ignoring the hours, minutes, seconds, and milliseconds and discard the time zone to make the write value take up less space.
With a local client side logging, you can't save it to a 'file' as none of the persistent filesystems are writable - you just have the roku registry, which is cleared on a factory reset.