What concentration of hydrogen peroxide kills mold?
The CDC Guideline for Disinfection and Sterilization in Healthcare Facilities provides a good overview of various disinfectants and their effectiveness against different kinds of pathogens, along with citations if you're interested in more detail.
This document doesn't evaluate the effectiveness of Hydrogen Peroxide against Stachybotrys (black mold) specifically (the CDC specifically recommends Chlorine Bleach for this purpose), but it does describe it's effectiveness as a fungicide. Note that the level of disinfection needed to control pathogenic fungus in a healthcare setting is likely much higher than needed to control black mold in a house, but it can give you a sense of how effective Hydrogen Peroxide is overall:

A 0.5% accelerated hydrogen peroxide demonstrated bactericidal and
virucidal activity in 1 minute and mycobactericidal and fungicidal
activity in 5 minutes [656]
...
A 7% stabilized hydrogen peroxide proved to be sporicidal (6 hours of
exposure), mycobactericidal (20 minutes), fungicidal (5 minutes) at
full strength ... [655]
...
The 7% solution of hydrogen peroxide, tested after 14 days of stress
(in the form of germ-loaded carriers and respiratory therapy
equipment), was ... fungicidal (&gt;5 log10 reduction in 20
minutes),[663]
...
A new, rapid-acting 13.4% hydrogen peroxide formulation (that is not
yet FDA-cleared) has demonstrated sporicidal, mycobactericidal,
fungicidal, and virucidal efficacy. Manufacturer data demonstrate that
this solution sterilizes in 30 minutes and provides high-level
...
Commercially available 3% hydrogen peroxide is a stable and effective disinfectant when used on inanimate surfaces
disinfection in 5 minutes [669]

From this, it seems like you'd want to use accelerated Hydrogen Peroxide, or 7% stabilize Hydrogen Peroxide to ensure fungicidal disinfection. 3% Hydrogen Peroxide is effective against bacteria, but the studies cited didn't test it against fungi.