You would need to change furnace types to a direct vent, and direct vent it out the basement via a 90 degree PVC pipe. And that assumes the pipe is a vent pipe, and not a main trunk line for the heat to move through the home. The brick would need to all be removed from the top down, repairing the roof, and each floor it went through. Many old homes had brick chimneys that had pockets for joist or rafter supports. You would need to assess if that was the case here. This is not a minor job. It's major work, and major expense.

No, not unless you move your furnace, and build an entirely new chimney. That would involve a whole lot of cash, because, it would have to be rerouted through the roof too. Sorry, but, that chiminey is necessary, if you want heat.. If your budget is huge, yes, it all can be moved around, at a big expense.

You'll have to call a HVAC contractor. You don't say what type of furnace you have and how old it is. Is it on an exterior wall? Maybe it can be directly vented to the outside through the wall. Does your hot water heater also use the flue? Are you going to gain more than the small area it takes up if you remove it? Were you planning on expanding the kitchen into another room on the other side of it? If so, couldn't you work around it? There might be way to make it look intentional. Draw up a floor plan on graph paper showing the adjacent spaces so we have a better idea what you're working with.

If you have or upgrade to a 90+ efficiency furnace, the exhaust flue can be 4" PVC which is easy to redirect, and even exhaust horizontally out of the basement. Same with water heater (or go electric). But, it all costs money!