The library you need is called libsurfaceflinger_client.so. You can pull it from any device running Gingerbread or higher version of Android, with command
adb pull /system/lib/libsurfaceflinger_client.so
On ICS or JB, class ScreenshotClient is part of libgui.so. The makefile for screencap which is the example of using ScreenshotClient, suggests that linker may need other libraries:
libcutils libutils libbinder libskia libui libgui
Also, the code of screencap.cpp goes as follows:
ScreenshotClient screenshot;
if (screenshot.update() == NO_ERROR) {
    base = screenshot.getPixels();
    w = screenshot.getWidth();
    h = screenshot.getHeight();
    f = screenshot.getFormat();
    size = screenshot.getSize();
} else {
    const char* fbpath = "/dev/graphics/fb0";
    int fb = open(fbpath, O_RDONLY);
    if (fb >= 0) {
        struct fb_var_screeninfo vinfo;
        if (ioctl(fb, FBIOGET_VSCREENINFO, &vinfo) == 0) {
...
This means that at least you must check that update() succeed. Unfortunately, unless teh device is rooted, the apps cannot be granted permission to read from /dev/graphics/fb0 and use the fallback of /system/bin/screencap or /system/bin/screenshot.