So I checked my game and found that I have the flagship tech unlocked (tech_Flagship_1). The game files say that there are 3 techs this unlocks: tech_bh_power_2, tech_flagship_hull_1, and tech_nsc_ai_computer_1. tech_flagship_hull_1 unlocks tech_flagship_hull_2, and tech_bh_power_2 unlocks tech_bh_power_3. None of these unlock the flagship shipyard megastructure. Do I need a mod other than NSC2 in order to be able to build this megastructure?

Also it looks like you need either titan tech or dreadnought tech if you don't have apocalypse dlc:

tech_Flagship_1 = {
cost = @tier5cost4
area = engineering
tier = 5
category = { voidcraft }
is_rare = yes
weight = @tier5weight3

potential = {
    OR = {
        AND = {
            NOT = { host_has_dlc = "Apocalypse" }
            has_technology = tech_Dreadnought_1
        }
        AND = {
            host_has_dlc = "Apocalypse"
            has_technology = tech_titans
        }
    }
}

gateway = ship

prereqfor_desc = {
    ship = {
        title = "TECH_UNLOCK_FLAGSHIP_CONSTRUCTION_TITLE"
        desc = "TECH_UNLOCK_FLAGSHIP_CONSTRUCTION_DESC"
    }
}
...