My main bathroom does not [yet] have an exhaust fan and I'd like to install
one. There is a ceiling light fixture that has two flood bulbs in it, one
regular and one heat bulb which we use when coming out of the shower. I was
thinking of replacing this light fixture with perhaps a combo light-fan unit
but I don't think they make one with a heat lamp in it.
So I could either purchase what I find on the net or in HD or keep the
existing light fixture and mount the fan between the fixture and the outside
wall.

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

Thanks,
Walter