I would say that the tone of this poem is most ironic in the first stanza. By the third stanza, it is not ironic at all -- it is angry.
In the first stanza, the tone is ironic because the words Holmes uses are opposed to what he actually wants. The first line of the poem is the most ironic. He certainly does not want the flag torn down.
But the tone of the third stanza is not ironic. He is saying that it would be better to put the ship out to sea and let it die a noble death than to have it be pulled apart by the "harpies of the shore."