The phrase "a basic conflict of" is correct and usable in written English.
It can be used to describe a fundamental disagreement or clash between two or more parties, ideas, or principles.
Example: "The negotiations broke down due to a basic conflict of interests between the two companies."
Alternatives: "a fundamental disagreement of" or "a core clash of".
More likely, it's going to come down to a basic conflict of personalities.
This conflict between these two visions of America — it's a basic conflict of values.
Many want and expect better-paying jobs on Wall Street after they leave government, and so are shrink-wrapped in a basic conflict of interest.
This surprise reflects, however, our anthropocentrism rather than a basic conflict of our conception of biological relationships.
There is a basic conflict between the goal of maximizing profit at every level and the goal of actually providing health care to those who need it.
Castle Bravo played a key role in establishing the deep fear of all things nuclear that persists to this day, helped give rise to modern environmentalism, and even planted the seeds of a basic conflict modern society is struggling with: Are the benefits of modern technology outweighed by the threats they pose to nature itself?
As we consider how we will be able to change our behavior and somehow recoup the loss to our environment on land and sea, we come down to a basic conflict over ownership and control of our natural resources.
The authors suggested that the CBP illustrated a basic conflict between state and federal control of water allocation and called for agency reform that would disentangle the rights of irrigation and hydropower, correct interstate externalities, and facilitate interstate water rights transfers if greater efficiency was to be gained in water use in the Northwest (Butcher 1986).
Secret partnerships were set up that critics say violated the most basic conflict-of-interest rules.
But the basic conflict at the heart of "Project Greenlight" -- and every aspiring screenwriter knows that there must always be a basic conflict -- was a familiar one.
Perhaps most disturbing, the game fails to invest the basic conflict of World War II with any significant weight.
