I always wonder if there’s anything in the world that hasn’t been invented yet ?… Difficulty in removing fallen bricks, tiles any other debris from a chimney flue
would depend on its shape and accessibility. There are tools designed specifically for cleaning of the chimney flue (check this page - http://whitecaps.com/docs/chimney_sweep_tools.html
- RoKleen® Grabber).
So the questions would be:
Can you safely get to the top of your chimney for an unobstructed view of its interior?
Is the chimney’s contaminated section visible? Servicing / removing fallen bricks from some chimney flues might be difficult because of their shape, i.e., corbelled chimneys.
Is it worth purchasing the tools required to remove bricks from the chimney flue instead of ordering chimney sweep services.
I don’t know how severely your chimney is deteriorated but falling interior bricks are usually signifying missing mortar and possibly missing chimney’s flue liner. It would make sense to get a professional and evaluate the chimney for its structural integrity / safety.