After reading about the blend modes more, which I don't have much experience with, I came up with this equation:
glBlendFuncSeparate(GL_ZERO, GL_DST_COLOR, GL_SRC_ALPHA, GL_ZERO);
glBlendEquationSeparate(GL_FUNC_ADD, GL_FUNC_ADD);
Testing it out on this website seems to show it working properly.
Note: The image being drawn over the framebuffer copies its alpha channel (not its greyscale colors) into the framebuffer's alpha channel. I can't make it use the source's RGB channel as the framebuffer's alpha, I don't think. I would've thought GL_SRC_COLOR instead of GL_SRC_ALPHA would've done that, but that isn't working in that preview website - it seems that when used for the alpha equation, GL_SRC_COLOR and GL_SRC_ALPHA do the exact same thing.