When, like committed linnets, I With shriller throat shall sing The sweetness, mercy, majesty, And glories of my King; (17-20)
Singing and poetry are often closely linked. Here, the speaker suggests that he will write a poem in celebration of his king, even though he is in prison. The rhyme on "king" and "sing" is interesting, for it suggests that there may be a close relationship between politics (the king) and art (song).
When I shall voice aloud how good He is, how great should be, (21-22)
To "voice aloud" one's opinion implies that lots of people will hear it. It also seems to be a metaphor for publishing poetry, or anything for that matter. A "loud voice" can be heard by lots of people; lots of people will "hear," or read, the poem when it is published.