In this case, the 「のに」 is about the 「声に出して逃がす」.
The role that 「の」 plays here is the same as 「こと」.
Example:食べるのに夢中である = 食べることに夢中である
So, to translate your example:
Even though she is hesitant from embarrassment, she seems busy letting escape vocalizations of the waves of pleasure
*Naruto pointed out that the 「逃がす」 in this example is transitive and therefore my initial translation was incorrect. I have corrected the translation to reflect the correction.
*It should be noted that my translation is still not 100% accurate, grammar-wise. What is being let escape is not 「声」, but 「快楽の波」. 「声」 is simply the method by which the escape is being let happen. I worded it this way because it sounds more natural, but the exact translation would be as worded by naruto in the comment below.