Are Adventist churches supposed to be under a conference or can they be independent?

Local Seventh-day Adventist churches are part of a local district, which is part of conference/union, which is part of a division, which is part of the General Conference of Seventh-day Adventists. The hierarchy may vary a little bit in different areas or divisions, but that is the general organization. If a church becomes "independent," it ceases to be a Seventh-day Adventist church. To put it another way, the Seventh-day Adventist denomination does not follow congregationalist polity (hence the term "denomination"), but instead it is hierarchical.