In a flash and Like a shot

In a flash adverb - Without any delay.

Like a shot and in a flash are semantically related In some cases you can use "Like a shot" instead an adverb phrase "In a flash".

Like a shot adverb - Without delay or hesitation; with no time intervening.

In a flash and like a shot are semantically related in fast topic. You can use "In a flash" instead an adverb phrase "Like a shot", if it concerns topics such as speedily, at once, very quickly.