I would recommend Fluteworld or FluteSpecialists Inc. if you are wanting to do a consignment. Consignment fees are rather hefty as previously mentioned and you also need to be cautious about leaving it in the care of the company you are working through. There are certain companies that have a history of poor management and dishonesty regarding consignments, but an excellent history of customer service from a buyer's perspective. So take that into consideration.
If you want to get the most cash out of it and are willing to wait long enough, you could just sell it yourself. It will take longer because you won't be able to reach as many customers and the market is not good for inline flutes (even if it is recently overhauled, inline flutes are not popular right now).
If I were you I would widen your net of companies to do consignments with (I'm guessing you contacted CN and were refused) because most would gladly take it on consignment. Just be careful. It's a shark tank and you're bait.