If you have access to it, I would do this in Illustrator
You can use Image trace to convert the image into vector shapes which you can then manipulate resize and recolour if required - all with nice smooth vector edges.
Section before image trace
After image trace - see smoother vector lines:
Showing paths :
I do have illustrator. What I do know is the original was created in Photoshop. I am unsure how to setup the file for screen print output
Will you be printing in CMYK, RGB or spot colours? Will there be white ink?
Trying to print spot colors. There may be a white, or it could be discharged.
In that case it really has to be redone in Illustrator, not only to get the colours separate, but also to make sure it is all vector. I've never worked with screen printing, hopefully someone can outline either the things that must always be done, or the technical questions you need to answer before starting.
I am unsure how to setup the file for screen print output
Make sure you talk to the printer before spending much time on this. Screen printing usually does not use halftone screens or process color, so there has to be a spot color separation for each color or transparent ink. Also depending on how the colors separate the trapping can be complex—screen printing needs a larger trap.
It wouldn't be impossible to do this with Spot Channels in Photoshop, but you really have to know the process. Screen printing is very different than offset, the inks are usually very opaque and you don't necessarily need vector art because the screen fabrics (not halftone screens) are so coarse.