How can the Scientific Revolution be seen as a conflict between authority and evidence?
The extent to which the Scientific Revolution can be said to be a conflict between authority and evidence is determined by how this revolution is historically framed. For instance, if one dates the beginning of the Scientific Revolution at Johannes Kepler's correct orientation of a heliocentric solar system and Galileo Galilei's further propagation of this idea, then--after Galileo was forced to recant his views because he used them to challenge traditional ecclesiastical teachings--the conflict between authority and evidence is obvious. (In actuality, it is not as obvious as is often thought; Galileo was, in some ways, inviting censure when, in the "Dialogue Concerning the Two Chief World Systems," he named the Church's spokesman Simplicius.)
On the other hand, if one orients the Scientific Revolution toward the latter half of the Rennaissance, with Francis Bacon--who conceptualized the scientific method--as its first revolutionary and Isaac Newton as the most important, then there is much less conflict between authority and experience. Newton held unconventional (Socinian) religious views, but this did not prevent him from lecturing at Cambridge.
Nonetheless, science itself is, by nature and methodology, always to one degree or another in conflict with authority that is inconsistent with experience. Experience (or the inductive method) is the basis of science. For this reason, while science does not exist to challenge authority, it often does.
The Scientific Revolution with its evidence in tow carried by men like Galileo, as well as many others posed a direct threat to the authority of the Roman Catholic Church. The conflict was rooted in the preservation of the societal status-quo with the church front and center and the human desire to explore new possibilities. For example, Galileo suggested an alternate perspective which was in conflict with church doctrine he was thrown in jail and put on trial. The power of the church had never been questioned until the revolution in science, and as such the church viewed science as the 'enemy' that had to be destroyed.