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The process of emitting a flow value from a separate function in Kotlin Coroutines involves the following steps:

1. Create a flow object using the flow builder function.

2. Use the emit() function to emit values from the flow object.

3. Create a separate function that returns the flow object.

4. Call the function and collect the emitted values using the collect() function.

For example, consider the following code:

fun myFlow(): Flow<Int> = flow {
    for (i in 1..10) {
        emit(i)
    }
}

fun main() {
    runBlocking {
        myFlow().collect {
            println(it)
        }
    }
}

In this example, the myFlow() function creates a flow object that emits values from 1 to 10 using the emit() function. The main() function calls the myFlow() function and collects the emitted values using the collect() function. The output will be the values 1 to 10 printed to the console.