Just had mine done (solid fuel stove with lined flue). The guys used a rotating rod and flail set bit like this:
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Never seen that before - but it brought down a large amount of clag - about 4 times what came out last year with a regular brush.
The thinner rods seemed to go round the bends pretty easily too.
At £45 a year for sweeping, I'm not really in a huge hurry to DIY this, but I was intrigued...