Brushless motor dynamics (BLDC transfer function)?
The picture below rapresents a block transfer function of a motor. It can be any kind of it, let we suppose it's about brush DC motor with permenent magnet. Any other type shall be transformed in the d,q coordinate system. For PMSM or BLDC this is done with Park and Clarke transformation.
The d-component is the excitation, a permanent magnet. The q-component is related to the torque, in DC brush motor is the armature component.
Thus, \$u_q\$ is the armature voltage, \$R_q, L_q\$ are resistance and inductivity of the armature, \$k_\Phi\$ is the flux constant (kv in your case, but with different units), \$M, M_L\$ is motor torque and load torque, \$J\$ is the moment of inertia, \$F\$ is the friction constant, \$\Omega\$ is the angular speed, \$\Theta\$ is the angle of the motor, \$U_i\$ is the back EMF voltage.
For better understanding you should look for Field oriented control, where you will find how a multi phase machine is transformed into a d,q model (brush DC motor with separate excitation), then all the copmutation is the same as DC motor.

EDIT:
The block diagram is reararanged in a equation using the property of closed loop rearangement. Let the open loop blocks rapresent \$G_1(s)\$ and the feedback path \$H(s)\$, which in our case is \$k_\Phi\$. The equivalent transfer function of the closed loop is:
$$ G(s)=\dfrac{G1(s)}{1+G1(s)\cdot H(s)}$$
This yields the transfer function of speed vs. voltage:
$$ \dfrac{\Omega(s)}{u_q(s)} =\dfrac{\dfrac{k_\Phi}{L_qJ}}{s^2 + s\dfrac{R_qJ+L_qF}{L_qJ}+\dfrac{R_qF+k_\Phi^2}{L_qJ}}
$$
$$ \dfrac{\Omega(s)}{u_q(s)} =\dfrac{{k_\Phi}}{s^2L_qJ + s{R_qJ+L_qF}+{R_qF+k_\Phi^2}}
$$
You may see it is a second order system.
EDIT:  from Anton Skuric's notes:  Corrected formula with missing F. The formula is valid for DC motor. For BLDC and PMSM the \$k_v\$ and \$k_i\$ are not equal, thus \$k_{\Phi}\$ should be split to \$k_v\$ and \$k_i\$.
EDIT: Separate voltage constant \$k_v\$ and torque constant \$k_i\$ instead of the same \$k_{\Phi}\$
$$ \dfrac{\Omega(s)}{u_q(s)} =\dfrac{{k_i}}{s^2L_qJ + s{R_qJ+L_qF}+{R_qF+k_v\cdot k_i}}
$$