It’s an open question whether this chiasm should be considered part of the first chiasm in the Flood narrative, or whether this is a separate overlapping chiasm in the same story — I’ve separated them here to make them easier to see and understand. The focus is the same as the first chiasm in the Flood narrative, the remembrance of Noah, and the turning point in the fulfillment of God’s promise to him.
A: Take with you seven pairs of all clean animals… and seven pairs of the birds of the heavens also… Genesis 7:2,3
B: For in seven days I will send rain on the earth forty days and forty nights… Genesis 7:4
C: And rain fell upon the earth forty days and forty nights. Genesis 7:12
D: And the waters prevailed on the earth 150 days. Genesis 7:24
But God remembered Noah… Genesis 8:1
D': At the end of 150 days the waters had abated… Genesis 8:3
C': At the end of forty days Noah opened the window of the ark that he had made… Genesis 8:6
B': He waited another seven days, and again he sent forth the dove out of the ark. Genesis 8:10
A': Then he waited another seven days and sent forth the dove… Genesis 8:12
You can see the 7->7->40->150->center->150->40->7->7 pattern clearly when the elements are arranged this way. The main problem with this chiasm is the two mentions of sevens in the beginning of the series — there doesn’t seem to be a perfect match at the end of the series unless you take the two pairs of sevens as one mention of the number seven (or I’ve missed another seven in the text someplace, which is possible). The chiasm is strengthened by the tying of the birds in A and the dove in A’, which may overcome this objection.