How can the following data regarding flower phenotypes be explained?
Because it seems you might be studying for a test, I will try to not answer directly but show the beginning of a chain of logic that might be more useful.

Let's review the very plain evidence. blue crossed against other colors leads to 3:1 ratios of blue:other. So it seems that blue is dominant in those cases. But when you cross those colors against each other, you get silly nonsense, a 3:1.2:1 ratio or something. 

So, based on the linked answers, you are justified in thinking that genetics determines flower color, just because of the simple Mendelian pattern of the first 2 crosses. But things don't work for a straightforward monogenic trait in the pinkxwhite cross. 

Let's now analyze your explanation. You say: "I was thinking blue (BB) was the dominant epistatic flower color allele—BB or Bb would give blue regardless of the other color allele, and bb would allow the expression of color dictated by the other gene..."

But look at the parents and offspring of the third cross. You say blue is dominant- but it is in fact expressed in the offspring of non-blue parents! So blue can't both be dominant and be the "controlling" epistatic gene. So now: let's consider some other similar possibilities:

1) blue = dominant and is controlled by another locus (recessive or dominant?)

2) blue = recessive and controls another locus (recessive or dominant?)

Do any of those hypotheses match the data?

A final observation: I find it always helps to add up all the combinations of phenotypes (if possible; for example the ratio of (blue+white) : pink, etc.) to see if anything looks like a familiar ratio.

I hope that is useful (and not too late to be helpful in studying, if that is your goal).