"Walter Cohen" writes:

Main question:
I could exhaust the fan straight out horizontally through the
outside wall.

That'd be my pick.

However, my kitchen is right next to the bathroom and a kitchen
ceiling fan, with duct work, leads straight up through the attic and
roof for venting. This kitchen fan duct is relatively close to the
bathroom and I'm wondering if instead of venting the bath fan
horizontally out the side of the house wall I could connect it up to
the kitchen fan duct which runs up through the attic to the roof.

Any thoughts on if this is advisable or might cause problems? I hardly ever
use the kitchen fan, by the way.

In this situation, kitchen fumes could be easily pushed into the
bathroom, and vice versa. As such, I'd be surprised if local codes
would allow it particularly given the grease-laden kitchen air's
likelihood of getting in contact with a bath exhaust fan that will
have large furry labels saying "not designed for kitchen use."

I *think* the reason for the labels is that unless a fan is
electrically designed to be moving greasy air, you can end up with a
fire hazard in a hurry, which I learned anecdotally:

Some exhaust fan specialist company in Chicagoland brilliantly
installed a bath fan in the ceiling over my stove which had lacked any
ventilation previously. A couple years after I had this fan added, I
started hearing arcing and fan stuttering. I powered it off, popped
the cover of the fan, and was immediately greeted by a big yellow
warning label "not designed for kitchen use." Ironically it was coated
with grease. I promptly wanted to throttle the company for installing
a big steaming fire hazard in my kitchen ceiling.

To their credit, all it took was one phone message to the company
explaining my discovery, my desire to have it corrected, that the
estimate contract specified a kitchen exhaust fan, and a subtle
friendly mention of the words "looming fire hazard" and "liability."

So in short, I'd play it safe and vent that baby out the side wall or
to its own dedicated roof cap.

Best Regards,
--
Todd H.
http://www.toddh.net/