Per kmixter's suggestion, install metrics headers under /usr/include/metrics.

src/platform/metrics/README

 Copyright (c) 2010 The Chromium OS Authors. All rights reserved.
 Use of this source code is governed by a BSD-style license that can be
 found in the LICENSE file.
 
 The Chrome OS "metrics" package contains utilities for client-side
 user metric collection. The collected data is sent to Chrome for
 transport to the UMA server.
 
 
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 - Add a dependence (DEPEND and RDEPEND) on chromeos-base/metrics to
   the module's ebuild.
 
 - Link the module with libmetrics (for example, by passing -lmetrics
   to the module's link command). Both libmetrics.so and libmetrics.a
   are built and installed under $SYSROOT/usr/lib/. Note that by
   default -lmetrics will link against libmetrics.so, which is
   preferred.
 
 - To access the metrics library API in the module, include the
-  <metrics_library.h> header file. The file is installed in
+  <metrics/metrics_library.h> header file. The file is installed in
   $SYSROOT/usr/include/ when the metrics library is built and
   installed.
 
 - The API includes two methods:
 
   bool MetricsLibrary::SendToUMA(const std::string& name, int sample,
                                  int min, int max, int nbuckets)
   sends a sample for a regular (exponential) histogram.
 
   bool MetricsLibrary::SendEnumToUMA(const std::string& name, int sample,
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 screen saver states to determine if the user is actively using the
 device or not and generates the corresponding data. The metrics daemon
 uses libmetrics to send the data to Chrome.
 
 The recommended way to generate metrics data from a module is to link
 and use libmetrics directly. However, the module could instead send
 signals to or communicate in some alternative way with the metrics
 daemon. Then the metrics daemon needs to monitor for the relevant
 events and take appropriate action -- for example, aggregate data and
 send the histogram samples.