Don't let the word "free" fool you. Just because this poem isn't working within typical formal constraints doesn't mean Brooks isn't laying down some serious formal poetic elements here. This poem is made up of four stanzas (a stanza is a group of lines—think of them as the paragraphs of poetry), of almost equal length. All but the second stanza are three lines long (the second is four lines long). Why Brooks threw that extra line in the second stanza is beyond us. We'd shoot her an email to find out, but she's been dead for a while now. It's likely she needed a little extra space to say what she wanted to say and wasn't going to let stanza length get in her way, just like she wasn't going to follow any sort of conventional meter with her turn to free verse here.
In each stanza, the end words of the first and last lines rhyme. For example, in the first stanza "plan" (line 1) and "man" (line 3) rhyme. In the second stanza (even though there are two lines in between instead of just one), "fumes" (4) and "rooms" (7) rhyme. In the third it's "in" (8) and begin (10). And in the final stanza, "minute" (11) and "in it" rhyme (13).
So what's the point of this rhyming? In this case, there are probably two reasons Brooks used rhyme. Reason 1: Rhyme lends a musical quality to a poem. So even if you have no idea what's going on in the poem—you're not sure of the meaning of the words, or what they all mean as a whole—it still… sounds nice. Rhyme is satisfying to the ear. Brooks knew that and made good use of it.
Not good enough? We knew you'd say that. Let us present Reason 2: rhyme is a good way of tying a poem together. If the rhyme scheme is consistent, and here it's almost perfect, then it gives the poem a sense of order. If, as readers, we feel a sense of order, we're more comfortable and receptive to the rest of the poem. The straightforward rhyme acts as a little gateway to the meat and potatoes of the poem. By the time we're lulled by the music of the rhyme, we're ready to dig in.
More than our comfort level, though, we'd say that the form and meter of this poem are, in the end, pretty darn spot-on in reinforcing the content and message of the poem itself. Think about it: free verse—with its unpredictable rhythms based in spoken speech—is way more appropriate to a kitchenette building than iambic pentameter. The setting here just doesn't seem like the kind of stuff you'd expect to find in a sonnet, right? And yet, that teasing rhyme scheme—which comes in at the start, disappears, then returns at the end of each stanza—seems to almost mimic the action of the dream. It's here for a second, then it goes, then it echoes again. Might the form that Brooks chooses here give us more reason to believe in our little white and violet dream?