I have a scissors jack where the top pivot is fixed and the links are all the same. The outer pivots move inward symmetrically with a known force via. a lead screw. Is there a formula for calculating the resulting downward force?

 

The force will change depending on the extension of the links. As they become extended they'll put out more force (or the handle will require less force to turn if pushing a consistent load).

You will need the pitch of the threads (angle of the applied load), the diameter of the crank (handle), length of links, as well as the force applied to the crank.

 

A Numerical simulation (FEA) will do it quickly and repeatedly with enduring accuracy during the design phase.

 

I think the FEA simulation is not necessary.

It is suffice a white paper sheet, a pen and the levers theory

 

OF course. FEA is never a necessity. It just help to lean your design faster when you go through several configuration... Which, as I understand Rambo3504 question, seems well to be the case.