What do you guys think of this? I've always liked free verse poetry because I like speaking a train of thought in a creative way and because I'm the vocalist for my band currently, how do y'all think free verse would work as lyrics? The problem I see with it is that there's no structure for it to flow musically.
For how can I give the King his place of worth above all else
when I spend my time striving to place the crown upon myself?
I feel like you'd have to write free verse while bearing in mind that it was going to be a song eventually.

It could work, you'd just have to be very conscious of the fact that what you were writing were going to end up as lyrics rather than train-of-thought poetry.
I've written poetry since as long as I could remember; 99% of it hides away because I'm from the school of thought that poetry should be expression of emotion with no audience, much like John Stuart Mill and other similar thinkers would argue, but this does carry over into my lyrics a bit, which, half the time, are highly similar to free-verse poetry. I just think that with free verse poetry as lyrics, you sort of need music without limitations as well. Obviously, the traditional musical structure will probably not work. I may be taking it too far, but I sometimes even find that I just can't even find chords that I like for parts and make up chords. There's a couple of examples of groups that I've found that seem to break traditional song structures and rely on free-verse poetry with some success. La Dispute features Jordan Dreyer, whom I think is a magnificent poet. You may not necessarily admire the music as a whole, but he often sings (if you want to call it that) free verse poetry perfectly.
some bands have managed to use free verse poetry as lyrics, even in traditional pop song formats. for example, fall out boy:

I'm gonna make it bend and break
It sent you to me without wings
Say a prayer, but let the good times roll
In case God doesn't show
Let the good times roll,
let the good times roll
And I want these words to make things right
But it's the wrongs that make the words come to life
"Who does he think he is?"
If that's the worst you've got better put your fingers back to the keys
One night and one more time
Thanks for the memories
Even though they weren't so great
He tastes like you only sweeter

-from 'thnks fr th mmrs'

as you can see no set rhymes or meter.

i'm moving this to S&L techniques, that's where it belongs.
I say, use your "free form" stuff as a laboratory. Then, take the promising bits and use them as the basis for a more structured lyric. I use my own poetry to find out what's on my mind and to give me a library of images/phrases to later use in songs. Hope this helps.
I know Snow Patrol and Eric Clapton use free form lyrics to great avail, although there is normally some meter in there...I'd reckon it really depends on whether you have the voice to pull it off. Rhyme does help the verses flow easier though,