Be careful about it, it is possible to do. BUT, usually people only put separate flues inside of an existing chimney because the old one leaks (usually gasses, not water). But they may just have high efficiency appliances and that could be the reason.
Either way you should know in a short time. If it leaks your house will reak like a skunk.
Just be prepared to add the filter immediately if you start to smell it, inside or out. let us know how that works if you do it.:thumbsup::thumbsup: