Why Dharma(धर्म) is pronounced as Dhamma in Buddhism?
Dhamma is the pali version of the word- In the time of Buddha , there was a conscious decision to record the teachings in Pali rather than Sanskrit. As sanskrit was not accessible to all and created a division between those who has access to it and who were interested in higher knowledge, but Pali was a common tongue in the region. 

But it is to be understood that Dharma(be it sanskrit or pali) in the context of Buddhism means much more than mere Duties as the common usage in Sanskrit means.
Dhamma is the very body of Buddhas teachings which is said to be universal in truth.