Even Later Answer
Get it using configuration like above.  I've found that this seems to require the provider assembly to be somewhere that the running program can find it.
    /// <summary>
    /// Creates a DbProviderFactory instance without needing configuration file
    /// </summary>
    /// <param name="lsProviderName">Name of the provider.  Like "System.Data.SQLite"</param>
    /// <param name="lsClass">Class and assembly information.  Like "System.Data.SQLite.SQLiteFactory, System.Data.SQLite"</param>
    /// <returns>A specific DbProviderFactory instance, or null if one can't be found</returns>
    protected static DbProviderFactory GetDbProviderFactoryFromConfigRow(string lsProviderName, string lsClass)
    {
        if (string.Empty != lsProviderName && string.Empty != lsClass)
        {
            DataRow loConfig = null;
            DataSet loDataSet = ConfigurationManager.GetSection("system.data") as DataSet;
            foreach (DataRow loRow in loDataSet.Tables[0].Rows)
            {
                if ((loRow["InvariantName"] as string) == lsProviderName)
                {
                    loConfig = loRow;
                }
            }
            if (null == loConfig)
            {
                loConfig = loDataSet.Tables[0].NewRow();
                loConfig["InvariantName"] = lsProviderName;
                loConfig["Description"] = "Dynamically added";
                loConfig["Name"] = lsProviderName + "Name";
                loConfig["AssemblyQualifiedName"] = lsClass;
                loDataSet.Tables[0].Rows.Add(loConfig);
            }
            try
            {
                DbProviderFactory loDbProviderFactoryByRow = DbProviderFactories.GetFactory(loConfig);
                return loDbProviderFactoryByRow;
            }
            catch (Exception loE)
            {
                //// Handled exception if needed, otherwise, null is returned and another method can be tried.
            }
        }
Another method that gets the Instance field directly from the assembly.  It works even when the DLL is somewhere else on the system.
    /// <summary>
    /// Creates a DbProviderFactory instance without needing configuration file
    /// </summary>
    /// <param name="lsClass">Class and assembly information.  Like "System.Data.SQLite.SQLiteFactory, System.Data.SQLite"</param>
    /// <param name="lsAssemblyFile">Full path to the assembly DLL. Like "c:\references\System.Data.SQLite.dll"</param>
    /// <returns>A specific DbProviderFactory instance, or null if one can't be found</returns>
    protected static DbProviderFactory GetDbProviderFactoryFromAssembly(string lsClass, string lsAssemblyFile)
    {
        if (lsAssemblyFile != string.Empty && lsClass != string.Empty)
        {
            Assembly loAssembly = System.Reflection.Assembly.LoadFrom(lsAssemblyFile);
            if (null != loAssembly)
            {
                string[] laAssembly = lsClass.Split(new char[] { ',' });
                Type loType = loAssembly.GetType(laAssembly[0].Trim());
                FieldInfo loInfo = loType.GetField("Instance");
                if (null != loInfo)
                {
                    object loInstance = loInfo.GetValue(null);
                    if (null != loInstance)
                    {
                        if (loInstance is System.Data.Common.DbProviderFactory)
                        {
                            return loInstance as DbProviderFactory;
                        }
                    }
                }
            }
        }
        return null;
    }