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My teacher says that it's not correct to answer the test
"How long (rain) yesterday?"
as "How long did it rain yesterday?"
She says there is only one way to do the problem with "how long" in the past tense with the Past Perfect Continuous. That is
How long had it been raining yesterday?
I think it's possible in a context where there is the point in the past which the Past perfect continuous relates to. But here without the context, I think the only right way is
How long did it rain yesterday?
As is often the case with aspectual distinctions in English (perfect or not; continuous or not) both are possible, depending on how the speaker is choosing to present the temporal structure of the events referred to.
How long did it rain yesterday?
is perfectly good if you are choosing to talk about yesterday's rain as a complete event.
How long was it raining yesterday?
works if you are choosing to talk about yesterday's rain as a continuing state.
With some context establishing a later viewpoint in the past, the past perfect can make sense; eg in reply to The roads were flooded this morning, you could use the simple perfect:
How long had it rained yesterday?.
or the continuous
How long had it been raining yesterday?
But in practice, English speakers tend not to use the past perfect when the temporal relations are clear, so I think most people would use the simple past or past continuous here. And, as you say, without that context the past perfect doesn't make a lot of sense.
How long was it raining yesterday?would allow the possibility that it was continuing into today or was possibly continuing from the prior day.