I just bought a house with an ICECO Weather King gas furnace (MOD# 80J07EAR01). The chimney/ fireplace is in bad shape and needs to come down. Currently the furnace is vented to one of the flues in the chimney. I am trying to find out what the venting requirements are for this unit (can I just pipe it through the wall? Do I have to go up past the roof? What type of pipe/insulated? Do I need to use?) So far I've had no luck getting info on this unit.

You will need to install a power venter to just go threw the wall. Or you can as you said run it all the way up the side o the house past the roof.