"Enambement", meaning: the running-on of the thought from one line, couplet, or stanza to the next without a syntactical break. It is a technique used in poems to make sentences or ideas flow across continuously through more than one line.

(An example of part of a poem which uses enjambement:
And She said he'd done
Something Very Wrong, and must
Stay in the school-room till half-past two.)

Now, I want to say a sentence like this in my essay:
"As in most free-verse poems, this allows the events to flow smoothly and *enjambment-ly*..."
but I'm not sure how to say that word; should it be "enjambed-ly" or "enjambment-ly" or what? The dictionary doesn't acknowledge "emjambedly". Would a using a hyphen work (enjambed-ly instead of enjambedly)? How could I do this correctly?

I have checked a dictionary and I can see your point about using enjambedly. It is not correct to use a hyphen to add the suffix -ly. I think you could use enjambedly but I think it sounds clumsy and therefore I wouldn't: that sentence would become the opposite of flowing smoothly.
Another way to approach this, if you really want to use enjambment, is to say
"As in most free-verse poems, *enjambment* allows the events to flow smoothly, ..."

I don't think it can - or should - be made into an adverb.
What about "...this enjambment allows the the events to flow smoothly."

I checked Dictionary.com & there is no way to make it an adverb. Maybe you should reword your statement & instead of describing the word meaning, just use the word!

enjambmentaly .