the chatter could be flywheel, could be the spring fingers on clutch pressure plate, could be thrust bearing, so replacing the flywheel and clutch together is a good idea and best practice, LUK and valeo do fair clutches and flywheels ,, or if were looking at putting a competition clutch system in it worth talking to C&G MOTORSPORTS they do all kinds of upgrades for all kinds of cars not sure what they do for mini but worth contacting them if want something better in there,
https://www.ebay.co.uk/itm/FOR-MINI...065189&hash=item2579a8969d:g:JcoAAMXQbcRQ8c~d
link below CG cover later cars added link so you could get contact info and a idea to what they do,, they are by far better than any standard clutch kit,, that said would not recommend fitting a paddle clutch on a daily used car start stop as are not nice,, but of have 500bhp to tame they are very good horses for courses..
there are solid flywheel kits but have down sides not as smooth as a dmf flywheel and can hurt gearbox and syncro