Loading Managed DLL   Firebirdsql.DataFirebirdClient.dll is ok
Loading Unmanaged DLL  fbembed.dll is not ok for embed

so easy way is not do embed.

DEMO APPLICATION 
Sure can run for
=====
http://www.codeproject.com/Articles/528178/Load-DLL-From-Embedded-Resource

1、want packget FirebirdSql.Data.FirebirdClient
tools -> NuGet manager - > manager NuGet
find FirebirdSql.Data.FirebirdClient install to project

2、reference -> FirebirdSql.Data.FirebirdClient.dll
a、copy local -> false
b、get full path [copy]
c、right click on Application1 -> add -> Existing item -> use b. path -> chooses file type dll -> find FirebirdSql.Data.FirebirdClient.dll  add
f、click reference -> FirebirdSql.Data.FirebirdClient.dll
Build Action -> Embedded Resource

3、open program.css
a、add using System.Reflection;
b、in main()  add
AppDomain.CurrentDomain.AssemblyResolve += CurrentDomain_AssemblyResolve;
c、copy this all

private static Assembly CurrentDomain_AssemblyResolve(object sender, ResolveEventArgs args)
        {
            Assembly assembly = Assembly.GetExecutingAssembly();
            //Project_Namespace.Package_Namespace.dll
            //Project Namespace = TestProject
            //Package Namesapce = Newtonsoft.Json
            using (var stream = assembly.GetManifestResourceStream(“FirebirdSql.Data.FirebirdClient.dll”))
            {
                byte[] buffer = new byte[stream.Length];
                stream.Read(buffer, 0, buffer.Length);
                stream.Flush();
                stream.Close();
                return Assembly.Load(buffer);
            }
        }

now run application for release, and see WindowsFormsApplication1\bin\Release
have .exe file, try to run.

======reference=====
http://ponyoth.hateblo.jp/entry/2015/07/28/072718

http://stackoverflow.com/questions/26179554/unable-to-access-embedded-firebird-database-server-with-net-client

http://www.sukitech.com/64/c-wpf-windows-form%EF%BC%8C%E5%B0%87dll%E5%8C%85%E9%80%B2exe%E5%9F%B7%E8%A1%8C%E6%AA%94%EF%BC%8C%E8%A3%BD%E4%BD%9C%E5%96%AE%E4%B8%80%E5%9F%B7%E8%A1%8C%E5%85%8D%E5%AE%89%E8%A3%9D%E6%87%89%E7%94%A8/

http://cyfangnotepad.blogspot.tw/2015/10/cnet-dllexe.html

https://support.microsoft.com/en-us/kb/319292#bookmark-5