Cooker Hood

I currently have a Cooker Hood with the exhaust venting through a 6" flexible aluminum pipe to the external wall. The pipe fixes with a 90deg bend directly into the hood, hidden by woodwork

I now want to fit a Cooker Hood with a Chimney which reaches to the ceiling. I am told the vent pipe would normally run under the upstairs floor and into the chimney so that it is totally concealed.
That would be directly under my bath upstairs !!!
This is totally impractical for me as I need a chimney...

Cooker Hood