The decay of the Bronx in the 1970s can be most directly attributed to post-World War II "urban renewal" programs spearheaded the New York Regional Plan Association. In the 1950s, New York City leadership wanted to establish Manhattan as the foremost center for commerce in America, which meant that the outer boroughs would be disregarded in favor of large government-funded building projects to uplift Manhattan. One of these extensive projects included the Cross-Bronx Highway, which urban planner Robert Moses would begin construction on in 1953. This project and the subsequent construction of new housing completely changed the socioeconomic demographics of the Bronx and prevented many of the communities who resided there from thriving.

Robert Moses' project displaced over 60,000 people, forcing many of them to migrate to areas like South Bronx or East Brooklyn. This significantly affected the economy, as many of the businesses in or around the path of the highway would either be abandoned or demolished for the sake of "urban renewal." At the time, the population of the Bronx consisted primarily of Italians, Irish, Jews, Blacks, and Puerto Ricans, and all of them were forced to fend for themselves, given only a sum of $200 in exchange for their residences. Upper and middle class whites were able to inhabit Levittown, a whites-only (literally archetypal) suburb established in New York, whereas working-class people only had the option of living in "towers-in-parks." This difference in relocation was the start of White Flight in the Bronx and significantly impacted the local communities in the Bronx because a) a substantial amount of the tax base left the Bronx and b) working-class (usually black and brown) people were left stranded in towers that lacked both infrastructure and private businesses.

In low-income housing projects like the Bronx River Houses and the Millbrook Houses, black and Latino newcomers often faced hostility from working class Jews, Irish, and Italians. As a result, several black and brown gangs were created to defend communities from harassment. Some of these, like the Puerto Rican Young Lords, were chapters of national organizations founded in other urban centers like Chicago. The conflict between these groups of people and the formations of the gangs themselves were coping mechanisms to address the impacts of construction on the Bronx: 600,000 manufacturing jobs were lost, and over 60% of young adults in the Bronx were unemployed. Meanwhile, White Flight got exponentially worse, and entire floors of housing in the Bronx were left abandoned. By the 1970s, over 300,000 people left the Bronx, and South Bronx's vacancy rates were one of the highest in America. Landlords recognized that realized that their buildings weren't making any money (because there weren't enough inhabitants), so they opted to neglect their tenants' needs by refusing to provide clean water or heating in the complexes. Some would even resort to burning their buildings down* and collecting insurance money, which resulted in the creation of the phrase "the Bronx is burning" (which I think is explicitly said on "The Get Down"). Massive citywide spending cuts allowed absentee landlords to further neglect their buildings, allowing for squatters and gangs to claim entire floors or even buildings. Of course, all of this had a Domino effect, so previously unaffected buildings were vacated when nearby buildings fell into absolute disrepair. Overall, ~40% of the Bronx was burned down or abandoned, which is why it looks like that in "The Get Down."

As for why DJs had "territories" (I'm referring to the question you commented below), you're partially correct. As I mentioned previously, many black and brown youth in the Bronx were members of gangs, so the DJs would often be banned from playing music or hosting block parties outside their gangs's sphere of influence. For example, Afrika Bambaataa (a character on the show and one of the Founding Fathers of hip-hop), was part of a street gang called The Black Spaces. However, as you can see on the show, Afrika would leave his gang to found Zulu Nation, a group who emphasized the importance of love over gang violence. Typically, DJs weren't drug kingpins or gang leaders (unless you count Afrika as being a "gang leader" of the peace-loving Zulu Nation), but they were still associated with gangs from their community (even if they weren't even in the gangs) because gangs were an integral part of life in the Bronx during that time period: every building had its own set of gangs. For example, in this article, Grandmaster Flash talks about how the Chandler Family, a local crime organization, inserted itself into his career once he started getting somewhat popular.

*The process for this was especially interesting but only tangentially related to the question, so I'll expand upon it here. Since everyone knew that the property value in the Bronx was insubstantial, landlords had to be very sneaky when they cashed out on fire insurance claims. They would create many different shell companies and have those shell companies purchase the buildings from one another at exorbitantly high prices and keep raising the price for each subsequent sale. This would artificially drive the property values up, making it ideal to take out insurance claims on. When landlords wanted to burn down the buildings, they would employ local gangs to strip the buildings of anything valuable (copper wiring, steel plates, etc.) and then burn the whole thing down with gasoline. Oftentimes, there would still be tenants or squatters living in the buildings, so many of them would die in the fires. In fact, there's still countless unsolved fire death cases today that are from the 1970s.

Sources:

Can't Stop Won't Stop: A History of the the Hip-Hop Generation (Jeff Chang)

The Hip-Hop Generation: Young Blacks and the Crisis in African-American Culture (Bakari Kitwana)

"Why the Bronx Burned" (Joe Flood)

Note: I recommend the above two books for anyone who wants to learn about the political and social factors that led to the birth of hip-hop.

Also, a follow-up question, what were the Cool Herc, Grandmaster Flash and Afrika Bambaataa territories about? Why did DJs had territories in the first place? Or, were they in fact drug kingpins / gang leaders or cover-ups for such?