The best pyro 3 build I can think of is Wiz Pyro 3 Thauma 2 WL2, full INT.
You’ll have warlock and pyro damage skills, with thauma’s buffs to help out your own damage and your party’s. Though I myself went Pyro 2 Thauma 3 instead, for maxing out the support side from Thauma (which’s stupidily good btw, just can’t forget to bring daino scrolls with yourself for group play).
Linker doesn’t work well with the low Skill facto (%) and multihit nature of most pyro and warlock skills (neither with random group play), given their very low amount of allowed hits.
Outside PvP (which’s a letdown by itself, let me start there), Kino has nothing really relevant to add to any wizard build IMO.
Sage is basically a Missile Hole buffer, and for PvP (especially our extinct GvG) it could be useful for zoning with fireballs, but that’s it.
If Drain gets relevant at Warlock 3, pyro’s enchant fire will have great sinergy with it. But besides that, both classes especializes in multihits, so both work well togetehr with + damage (like that of enchant fire, blessing, sacrament etc. ).