Drifter

[Collapsed We Swear]

Threads of fate cinching tightly
Weaving us together flesh to flesh — I don't think the words "fate" or "weaving" should ever be used in a contemporary poem. I know ordinary nouns and verbs can't technically be "cliche", but using "fate" or "weave" in a poem, without joycean levels of skill and self-awareness, is at the very least lazy.
Laid bare backed on bedrock 
Building our home —despite what I just said, I actually like this opening. "Cinching" is a brilliant choice of word in this context. In fact, this whole opening stanza, regardless of the cliches, is well done. And obviously the cleverness and originality of "laid bare backed" helps nullify the previous cliches. 

But how can I be a stone
With a heart shaped flake — flake? I'd find a synonym for that if I were you. 

An easy going smile —Cliche.
My prized poker face — Cliche.
Your heart bursting with passion —Cliche.
Is easy to throw away —Cliche.

I'm numb to the pull
A stray told to stay —I like this line "a stray told to stay". You obviously like internal rhymes. They rarely work. And I'm not entirely convinced this one works within the entirety of the poem, but I still like it.

Subject to parallax —Luckily, I know what parallax is, but I still had to look it up after reading this, just to make sure. So, if you are writing poems for people to pat you on the back and congratulate yourselves on how clever you both are for remembering a word you heard once, then keep it. But if you want someone to read this and actually feel something, maybe try another line. 
A lonely shooting star—Shooting star? Seriously?
Not meant for your hands
And too far for the heart

Hang on a little longer
Anchor to the deep
Or restless wings will carry me
Away in my sleep

Remind me to stay
When I long to leap

Silt slips through fingertips
And so can I

Hold me tighter
Until the old me is gone—All the rest is good. I didn't want to like it. But ultimately I did. But, read more poems. Don't fall for cliche (even though it sounds good) and read loads of Joyce and Beckett.