Can frequent ankle or bone related injuries lead to cancer?

No: There is no known relationship between bone or joint trauma and cancer.

See below: As far as my training has taught me, injuries don't induce cancers. These occur due to random (and many genetically programed) genetic changes that alter the dna in specific places that then cause unrestricted cell growth due to a variety of mechanisms. If for some rare chance during an injury a gene in a cell suffers a specific mutation that causes the unrestricted growth, a cancer could occur.