The comments below are not intended as an exhaustive analysis but provide a number of starting points.
You can look at the poem as working in two semantic realms: nature and society. Western society tends to push social groups that don't fit the categories "white", "male" and "middle class" towards the periphery and sometimes towards the realm of "nature". This also applies to people with mental disorders (and to anyone who is considered less intelligent). Fire, hunger (the verb "eat" is repeated several times in the poem) also belong to the semantic real of nature.
The poem plays with this tension between nature and society. For example, fire is compared to a "guest", and "guest" as a concept belongs to the realm of society. The poem's narrator addresses the fire as if it were a being capable of language. The fire's behaviour is described in terms that would fit the behaviour of a human being: "do not go upstairs", "eat (...) for breakfast", "eating (...) for dessert", "the fire's whole family had moved in".
The poem also uses language that is degrading towards the people staying in the psychiatric hospital. First, it calls the institution a "insane asylum", a term that went out of use in the first half of the 20th century, after academics had started studying mental disorders in a more scientific way. (For example, at Penn State University, the Chair of Mental Diseases was established in 1901. In Scotland, the Montrose Lunatic Asylum was renamed to Royal Asylum of Montrose in 1913 and to Royal Mental Hospital of Montrose in 1948. These changes took place several decades after Elizabeth Packard, who had been accused of insanity in 1860, had started the Anti-Insane Asylum Society in 1868. These are just some (almost) random names and events from the history of psychiatry.) However, the disappearance of the term "insane asylum" does not imply that everything is for the best now: the poem's narrator, who is in charge of the "insane asylum" still calls one of its patients "a dementia praecox", which is a dehumanizing use of language. (In this context, one might have a look at the anti-psychiatry movement of the 1960s and 1970s.) And the narrator uses the terms "insane", "maniac" and "lunatics" throughout the poem.
The fire that "eats" the "insane asylum" can be seen as an element of nature that burns everything that society has put in place to take care of the mental hospital patients. According to the view that puts such patients in the real of nature, this may be seen as a kind of liberation. But what is probably more important is that the poem's narrator, who is in charge of the hospital, humanizes the fire while using degrading terms for the patients. This may suggest that the whole mental hospital business is a kind of lunacy. This is strengthened by the psychiatrist/director's comment to the fire, "Hey, that’s where the dusts have built their cities," which doesn't appear to have rational explanation.
(A complete analysis of the poem should also discuss its wordplay and allusions. For example, "eat a log" versus "I could eat a horse" (and visitors to the hospital may be requested to sign a log), "war of nutrition" instead of "war of attrition", "lunatics out of the attic" versus The Madwoman in the Attic.)