does this have any relationship to second segment climb performance?
Only in that generally, second segment will be better the less flap that one has, but one might need a higher flap setting to carry the better load off the available runway. It's a compromise. The 717 has a requirement for minimum of 5 degrees of flap for takeoff, and a variable flap selector that allows anything up to 20 degrees for takeoff.
Whereas my understanding of windshear escape is that all segments go out the window, and one uses all available power, and the highest AoA possible - without stalling of course to out climb a severe downdraught. Fortunately my experience to date is limited to simulator models, and I hope it stays that way.
