Vent room air to the outside

Aside from the fact that your attic can be very dirty, you need to be concerned about the following:

• If you have any gas heating equipment in the attic (central heat, water heater(s)), they may not meet regulations to allow them to be connected to the house's main air supply. You can run a major carbon monoxide (CO) risk from improper ventilation of gas-burning equipment.
• Pest control companies can use harsher "dusting" pesticides in attic spaces - stuff you really don't want joining you in the house. Insulation is often loose and can irritating. If you have a much older house that might have asbestos insulation, then you have other problems as well.
• When you pull air out of the attic, it's repopulated by the air from outside. If the air outside is very cold, your attic could reach new low temperatures, freezing pipes or causing other damage. (This may or may not happen, but it's something I would make sure of before attempting this.)

You'll increase energy costs and only make it marginally cooler. The only way this could work is to fully insulate and make it part of the conditioned space. But the kitchen ceiling/attic floor is not designed to support any kind of real loads, so it's only practical to store very lightweight items anyway.

So what lightweight items can you store there? If conditioned space, anything that will fit through the access. If not conditioned, only items that can withstand extreme heat without degradation could be stored there. I would not store any valuable clothing in that kind of environment.