I have been working on a story on and off for longer than it should be, considering how little I actually have written. While I would love to get feedback on what I have so far, it is not a linear path through what the story will ultimately be (at least what I envision it to be). What do you recommend when posting a story as a work in progress? Does it need to be in its final, linear format or can it be scenes from throughout that have been written when the muse descends? Hopefully my question makes at least a little sense. Any guidance is appreciated!

I would recommend finding a beta first. That way you can receive feedback and get some help fleshing out your story. Of course you can also post it. The boards have been used for unfinished works before. But the way you describe it, you'd profit more from a beta reader.