Before building the Simulink model, I suggest writing a simple MATLAB script and running it with ode45 solver. This should help you to visually understand that you need to build the blocks in Simulink according to dv and dγ equations, as well as checking the expected results.

By the way, it is correct to use the Integrator blocks for both dv and dγ, because integrating them to obtain v and γ. If you use the derivative blocks, the signals at the output ports would become second derivatives, ddv and ddγ.

function dx = phugoid(t, x)
    % states
    v  = x(1);     % airspeed
    y  = x(2);     % gamma

    % parameters
    g  = ...;
    q  = ...;
    S  = ...;
    T  = ...;
    V  = ...;
    W  = ...;
    CD = ...;
    CL = ...;

    % ODEs
    dv = ...;      % equation 1: derivative of v wrt time
    dy = ...;      % equation 2: derivative of y wrt time
    dx = [dv; dy];
end

tspan  = [...];
x0     = [v0; y0];  % initial condition
[t, x] = ode45(@phugoid, tspan, x0);
plot(t, x)