else if (bitIndex > binValueList.Count)
{
result.Append(binValue.Insert(0, "1"));
}
in this line you add one bit in the beginning of result, But tests can be like this: FlipBit(127,17).In that case you should flip 17th bit of 8bit number, but in your code you flip 9th bit

forum is not dead!)
on that line -> if (binValueList != null && bitIndex <= binValueList.Count) you check for bitIndex <= binValuelist.Count,
but test cases can be like this : FlipBit(1,2) and bitIndex can be > than binValuelist.Count,
so your result become empty and in that line -> int testBin = Convert.ToInt32(result.ToString(), 2); you have error.

Thank you.