If its been working fine for years and the heat exchanger is making noise at a high temp then it may well be starting to choke slightly, doesnt take much on these to start off noise issues. (can also be a slow pump) unfortunately theres no absolute method to identifying what one is the issue (without expensive trial and error parts replacement) However chances are its probably a mixture of both.
Thermal stores (sludge buckets as their know) are fantastic bits of kit, except for the fact they essentially store loads of system debris and distribute it around the system while being notoriously difficult to clean fully.
As said, powerflushing can only be done on the radiator circuit, not the store, and powerflushing wont be effective on microbore generally.
Its certainly worth running some cleaner through it.
If your going to use X400, 3 bottles minimum for your system (no point spending the money and doing half the job) Drain system, fit filter to the return pipe of the boiler, add in the 3 bottles and refill allowing at least 2 weeks of running for best results. Try not go too much longer as some of the material will start to fall out of suspension much after that.
Drain the system (including opening all the radiator bleed points to let air into every radiator so that the water will fully drain out them all)
Refill, start circulating and then empty again, Ideally in your system your going to need to repeat this 3 or 4 times to A. get as much crap out the store as you can, and B. Dilute any cleaning agent down enough to the point where its no longer going to mix with other chemicals and cause problems.
Then finally redose with 3 bottles of inhibitor.
You can during the 2 weeks clean the filter out as much as you like, what filter are you going for?
I've had quite a bit of success on reducing and stopping noise issues with cleanser on stainless coil heatexchangers like yours, but if it doesnt work it would be a new heat exchanger (pricey and another 3 bottles of inhibitor again most likley)
FYI, your system is indirect. Direct and InDirect reffer to how the Hot Water is heated, although your thermal store is directly heated with circulating boiler water, the Hot Water for the taps is InDirectly heated via a coil in the store so its ok to use chemicals.
(Disclaimer - the above is not the best way to flush the system, but its the most viable for a DIY attempt)