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Here is one way to eliminate the elements in a flat array that exist in a column within an array of objects:

1. Iterate through the array of objects and extract the values from the column that contains the elements you want to eliminate.
2. Convert the extracted values into a Set to remove duplicates and make searching faster.
3. Iterate through the flat array and check if each element exists in the Set created in step 2. If an element exists, skip it; if it doesn't exist, include it in the new array.

Here's an example code snippet:

const arrayOfObjects = [
  { id: 1, name: 'John' },
  { id: 2, name: 'Jane' },
  { id: 3, name: 'Bob' }
];

const flatArray = [2, 5, 6, 3, 4];

// Extract column values from arrayOfObjects
const columnValues = arrayOfObjects.map(obj => obj.id);

// Convert columnValues into a Set
const columnSet = new Set(columnValues);

// Filter out elements that exist in columnSet
const newArray = flatArray.filter(elem => !columnSet.has(elem));

console.log(newArray); // Output: [5, 6, 4]

In this example, we want to eliminate elements in the flatArray that match id values in the arrayOfObjects. We extract the id values from the arrayOfObjects and store them in columnValues. We convert columnValues into a Set for faster searching and store it in columnSet. Finally, we iterate through the flatArray, check if each element exists in columnSet using the has() method, and include it in newArray only if it doesn't exist in columnSet. The resulting newArray has the elements [5, 6, 4], which are the elements in the flatArray that do not exist in the arrayOfObjects column.