Rhyme scheme? Meter? We don't need no stinkin' rhyme scheme. And this poem certainly wants nothing to do with meter. This is Mary Oliver we're talking about, and in The Leaf and the Cloud, she's about as loosey-goosey as it gets. The line lengths change a lot throughout, and in the second section, the thing practically looks like prose.
But that's not to say that this poem doesn't use form to its advantage. In fact, those sections are the way in which the poem organizes itself. It makes its own rules. And even though the sections look different, there are a lot of connections going on between them. Section 6 rolls right on from Section 5, talking about our speaker's parents. Section 11 recalls Section 2, picking up the story thread about the barn. Section 8 picks up the thread from Section 1 about what a poem is (or isn't). You might want to reread the poem and see what other connections you can make.
Breaking the poem up into sections makes us think that our speaker will be tackling different ideas. Starting a section with "Therefore" (Section 10 ) or "Anyway" (Section 11) kind of undercuts that point. The nature of transitional words like "therefore" and "anyway" is to bridge the gap between ideas. So in this way, the sections are not entirely distinct, because those words provide a sense of reaching back to what was just said. Oliver may be breaking this thing up, but there's no denying that it flows.
Breaking the poem up like this while keeping up the flow also seems like a way to let our speaker cover more ground without confusing us. It allows her to jump from present to past, from imagination to memory, from a meditation on poetry to advice for how to live. And those sections provide a sense of breathing room, so we can take things one idea at a time and not worry about holding it all in our mind.
While we're at it, we'd be remiss if we didn't remind you that "Flare" is the first poem in Mary Oliver's book The Leaf and the Cloud, which is itself one big poem. The book as a whole kind of works like these sections work, allowing her to jump around in time and location while still meditating on the themes of loss, observation, celebration of the world, love, sadness, nature, and all that poetry jazz.