as far as i know military labs do not help the construction speed of ships, there may be a researchable tech to speed up ur ship building speed (i'm not 100% sure i don't have sins open in front of me)

u can increase the amount of ships u build at once though,

for example :

if u have one frigate construction factory and u want to build ten ships, it will build one at a time.

if u have two frigate construction factories, and u want to build ten ships, each factory will build one ships at a time, so they build to ships

so technically u are now building ships twice as fast.

-Fes

There is actually a slight increase in ship building speed with the building of each military lab.

The TEC civ tree has a tier 7 tech that decreases ship building costs Lvl. 1 it's 17%, 2 is 33%, 3 is 50%, combining that with the other hull and shield increases, along with the TEC's stronger economy means that they're able to outproduce anything, assuming you aren't playing against a Vasari with Returning Armada.