How does the use of the below devices and structure help achieve the purpose of second chapter of The Narrative of the Life of Frederick Douglass?

As you have already outlined, an important purpose of the second chapter of the Narrative of the Life of Frederick Douglass is to address the use of slave songs and to deconstruct the white myth that the singing of the slaves implied that they were content and happy. 
Douglass describes how the slaves who had been chosen to go to the Great House Farm would sing "wild songs, revealing at once the highest joy and the deepest sadness" and how odd this music was in that "the most rapturous sentiment" would be sung in "the most pathetic tone" and vice versa. The diction and tone with which Douglass describes the experience of listening to these songs is one of both puzzlement and profound emotion:

The hearing of those wild notes always depressed my spirit, and filled me with ineffable sadness. I have frequently found myself in tears while hearing them. The mere recurrence to those songs, even now, afflicts me; and while I am writing these lines, an expression of feelings has already found its way down my cheek. 

Douglass is clear that this music represents the painful, sorrowful existence of slaves who are dehumanized by their status at the hands of cruel white masters. Although the jargon of the songs doesn't necessarily make sense, the implications of their soulfulness does: the life of a slave is a life of misery. It is thus deeply ironic that people (largely, one must assume, white people) have misinterpreted the songs as signifiers of joy. Douglass clarifies:

The songs of the slave represent the sorrows of his heart; and he is relieved by them, only as an aching heart is relieved by its tears... The singing of a man cast away upon a desolate island might be as appropriately considered as evidence of contentment and happiness, as the singing of a slave; the songs of the one and of the other are prompted by the same emotion.

This mythology/misinterpretation is ironic for that very reason--the act of singing is not a sign of contentment but a means of unburdening oneself of the great horrors of enslavement. 
Structurally, these realizations are clarified in the way that Douglass logically presents this information. He first establishes the parameters of life as a slave (the cruel punishments, the poor living conditions, etc.) and then leverages this knowledge to point out the improbability that any slave would be joyfully singing in such a situation. Through diction, structure, and the acknowledgment of irony, Douglass makes a very effective and moving argument about the lives of slaves.