How did Bohemia (a former kingdom) become associated with the style of hippies?

Racist stereotypes and cultural appropriation, the breakfast of champions!

The French have used the term bohémien to refer to the Roma since at least the 18th century, although the idea at its root goes back to their first appearance in Western Europe in the early 15th century. Claiming to ultimately hail from Egypt or "little Egypt" (hence the English corruption "gypsy"), in some towns and countries some of them presented a 'letter of passage' purportedly from Emperor Sigismund granting them the right to steal (!). The importance here being, he was also then the king of Bohemia, at least in name. (15th century Bohemia kinda loses the Hussite Wars and then kinda proceeds to act like it won them...It's Complicated.)

Unfortunately, I'm not firsthand-familiar with the medieval French sources, so I can't tell you if the appellation itself goes that far back; Aimee Kilbane cites it from a 1724 history of Paris so it's almost certainly a good deal older.

Kilbane also hypothesizes that already when Sauval used it, bohémien was already starting to take on metaphorical connotations related to stereotypes of the "Gypsy" life (as I will hence call it, following scholarship). However, for its alignment with artists living our la vie boheme, we have to turn to the 19th century.

In the early 19th century, the artists and poets of the Romantic movement cultivated an image of themselves as outsider-insiders--living separate and exotic lives but firmly within modern Western civilization, here namely Paris. Victor Hugo's secondary protagonist of Notre-Dame de Paris, note, is a writer enamored with a Gypsy woman. (Hugo is on record as saying the real central character is the cathedral). Just a few years after Hugo produced the source material for the most brilliant song in the Disney canon, in 1834, a French encyclopedist used bohémien outright to describe the artist community of Paris.

This is relevant to hippies in the 1960s, I promise.

Kilbane stresses the idea of "noncomformity" at the root of 19th century artists' and writers' adoption of the term bohemian. Looking deeper into the ethnic stereotype as well as 19th century poets' use of the term, however, other scholars sketch out how bohemian/Gypsy becomes a white Western European shorthand for the raw/primal/Nature aspect of humans. As Philip Landon puts it, using "Gypsy" to refer to the literary stereotype:

Idealized, the Gypsy is an innocent child of the universe leading a carefree life under the open sky, a living symbol of freedom in nature. Vilified, the same Gypsy becomes a primitive who has failed to rise out of nature: a lying, thieving, dirty, work-shy, promiscuous savage who abducts children and even engages in cannibalism. Both caricatures identify Gypsies with nature, conceived as a realm of antisocial self-interest irrevocably at odds with civilization.

Landon shows how 19th century poets would call their work "The Gypsy Scholar" and such, without having any either stereotyped Gypsies or actual Roma figures in the poem--that's how strong this impression of the Gypsy/"bohemian" already was.

But obviously there are no hippies in 1834, and not even in 1896 with the premiere of Puccini's La Boheme. What there are, however, are hippies in the 1960s and 1970s--which coincided with an upsurge in western Europe of Travelers, and especially of migration of Roma into the west and Italy in particular.

White hippies and the Roma shared a lifestyle and purposeful construction/maintenance of an identity separate from mainstream Western culture--and the hippies were aligned even more closely with the Gypsy stereotype than they were actual Roma. Freewheeling sexuality, singing and dancing, distinctive dress, spectacle for the sake of spectacle...

Hippies adopted less the "artist" part of the bohemien stereotype, and rather more the outsider/primal/spectacle end of things. However, the stereotype of the "bohemian artist" definitely kept the linking of the terms alive during the 19th and 20th centuries.