Don't think it will plug into the rdc300 ?Get a mk6 radio ... cheap on eBay, better looking and has the aux input that will take the item you posted ... I bought one and works
https://www.ebay.co.uk/itm/322563517738https://www.ebay.co.uk/itm/263050027034These also show track and artist info while playing the radio and I'm sure you can add a cd changer too !