Rationales may differ, but an advantage I see is that hexadecimal reminds you: “Okay, we’re not dealing with numbers in the arbitrary human-invented world of base ten anymore. We’re dealing with bits – the machine’s world – and we’re gonna play by its rules.” Hexadecimal is rarely used unless you’re dealing with relatively low-level topics where the memory layout of data matters. Using it hints at the fact that that’s the situation we’re in now.
Also, i’m not sure about C#, but I know that in C x << y is a valid compile-time constant.
Using bit shifts seems the most clear:
[Flags]
public enum MyEnum
{
None = 0,
Flag1 = 1 << 0, //1
Flag2 = 1 << 1, //2
Flag3 = 1 << 2, //4
Flag4 = 1 << 3, //8
Flag5 = 1 << 4 //16
}