How to write to the debugging stream?

You are writing into a stream pointer (ostr) instead of writing into a stream (*ostr). Try this instead:

    (*ostr) << "Some random text";

BTW, I do not think you need to surround libecap::MyHost() with parens.

I get different error:
adapter_minimal.cc:168:49: error: invalid use of incomplete type ‘class libecap::host::Host’
 std::ostream* debug_stream = (libecap::MyHost()).openDebug(6);
                                                 ^
In file included from /usr/local/include/libecap/common/registry.h:6:0,
                 from adapter_minimal.cc:4:
/usr/local/include/libecap/common/forward.h:32:8: error: forward declaration of ‘class libecap::host::Host’
  class Host;
        ^
adapter_minimal.cc:169:17: error: expected constructor, destructor, or type conversion before ‘<<’ token
 (*debug_stream) << "Global debug message from simple adapter";
                 ^
adapter_minimal.cc:170:20: error: expected constructor, destructor, or type conversion before ‘.’ token
 (libecap::MyHost()).closeDebug(debug_stream);
                    ^
adapter_minimal.cc:166:19: warning: ‘Registered’ defined but not used [-Wunused-variable]
 static const bool Registered = (libecap::RegisterService(new Adapter::Service), true);
                   ^
make[2]: *** [adapter_minimal.lo] Error 1

The "incomplete type ‘class libecap::host::Host’" error means you forgot to #include "libecap/host/host.h".

The "expected constructor, destructor, or type conversion" errors are a side-effect of the above error.

The "defined but not used" warning may go away after you fix other errors. If it does not, you may ignore the warning OR find a compiler-specific way to quiet it.