When Flush, at one point, is dognapped, Woolf uses the event as a way to illustrate the marked differences between English social classes. Flush observes the dire squalor in which he now finds himself, and remarks upon the violent behaviors of his captors, who require a high ransom payment in exchange for his return. With limited opportunities for them to be educated and earn a living, the community of people in the slums of St. Giles have turned to extortion in order to obtain money. When Flush makes comparisons between the brutal slum and Elizabeth Barrett's comfortable upper-class home, you can see the author commenting on British poverty and classism.
When Elizabeth and her husband Robert move to Italy, Flush remarks on the canine societal differences between that country and England. Most of all, he notices that all dogs are treated as equals; there are no hierarchies based on breed, lineage, or conformity to a standard of appearance and temperament. That is, of course, allegorical to the author's understanding of English aristocracy as absurd, because it is based not on individual merit but rather the luck/misfortune of being born to a set of parents, whomever they happen to be.
On one level, Flush is a sweet, pseudo-biography of Elizabeth Barrett Browning's pet spaniel, creatively written but structured around factual information drawn from the poet's letters and other collected writings. On another level, the book is a critique of then-modern English society. The ways that Virginia Woolf writes Flush's interior monologues and observations, and - because Flush is inherently non-human - he is a continual foreigner in his world. This canine naivete allows Woolf to comment on the socioeconomic and class divides that were so rigid and prevalent in England.
Librorum annis