How to calculate minimum flying speed in distributed propulsion?
The better way to look at predicting the performance of a distributed propulsion wing (specifically the NASA X-57 wing concept) is to think of the propellers along the span as a high-lift device that augments the lift of the wing through interaction with the trailing-edge flaps, rather than as headwind-generators. In other words, the propellers increase wing C_L, allowing you to have a smaller wing for the same landing and takeoff distances.

With many small propellers, you get performance that starts to resemble a jet flap or externally blown flap, but without the complexity of internal ducting or non-uniformity due to a small number of engines. 

Optimistic rule of thumb from thin airfoil theory is that, for a 2D section
$c_\ell = \frac{\partial c_\ell}{\partial\alpha}\alpha + \frac{\partial c_\ell}{\partial\delta_F}\delta_F$

$\frac{\partial c_\ell}{\partial\alpha} = 2\pi(1+0.151\sqrt{c_J}+0.219c_J)$

$\frac{\partial c_\ell}{\partial\delta_F} = 2\sqrt{\pi c_J}\left(1+0.151\sqrt{c_J}+0.139c_J\right)^{\frac{1}{2}}$

where $c_J = 2\frac{h_J}{c}\frac{V_J}{V_\infty}$

$V_J$ can be calculated from propeller momentum theory based on disk area, input power, and assumed efficiency. 

Bear in mind this is for section $c_L$, and will need 3D corrections for the whole vehicle based on percentage of span with propellers, induced flow, etc. It is also reasonable only in the limit of small flap deflections and angles of attack. Wind tunnel data or flight test reports might be a better place to get a first-pass estimate.  

https://www.researchgate.net/publication/299641308_Comparison_of_CFD_and_Experimental_Results_of_the_LEAPTech_Distributed_Electric_Propulsion_Blown_Wing

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19740003719.pdf

https://arc.aiaa.org/doi/abs/10.2514/6.2019-3170