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Considering that magnetism is a force, I very well understand that we only want the force that is pushing in the direction of the infinitesimal surface and keeping in mind the definition given before, it seems much logical to me to use this :

$$\iint_S \frac{\mathbf{B}\cdot\mathbf{dS}}{|\mathbf{dS}|}$$

We find the direction with the dot product but take off the surface and then we sum up the force. I probably am misunderstanding the flux definition and hope someone would have the kindness to clear this up.

I understand this integral can't be done since we no more have an infinitesimal to integrate with respect to it, but I think you see what I want to say through it.

My problem with this is that when I'm thinking that we're kind of distributing the force over that ##|\mathbf{dS}|## we'll be loosing "strength", ##|\mathbf{B}|*0.00000000.......1##, I hope you're getting what I mean.

Thank you for your time!