Well, I think that's a "Coin-Flip-Situation". JK could as well just have shown us these memories to show us that Snape had a very hard childhood and also adolescence. Hence his bitterness.
But if you are right, it means 2 things. First, his father must still be alive - otherwise he wouldn't be that afraid of him. Second, his father has to be a) more powerful than him and b) highly involved with Voldemort - I think these criteria have to be met in order of Snape to fear his father in a "Boggart-like manner"?
In that case it's quite odd JK only mentioned Snape's father once.
I'm rather sceptical about that possibility 😉
Maybe his greatest fear actually is Voldemort killing him? Assuming Dumbledore is right about trusting Snape, what could a former Death Eater fear more than his old master catching him? I just reread the two Occlumency scenes in Phoenix, and in one sentence (P.470) Snape tells Harry off for speaking the Dark Lords name, while Snape still refers to him as "the Dark Lord".
Fear of Voldemort could explain why Snape still is reluctant to speak Voldemort's name, hence supporting the possibility of Voldemort being Snape's Boggart.
On the other hand, Snape still calling Voldemort "The Dark Lord" could be treated as evidence that Snape is a doublecrosser and still in Voldemort's service. Assuming this to be true Snape should rather fear Dumbledore finding out, hence Snape's Boggart taking the form of Dumbledore.
What do you think?
Wow, that got long - hope it makes sense 😛