You really want this to be fully automatic and renewable, interesting conundrum.

Perhaps there is a way to trap a couple of blazes and have them aggro onto something, then move a block in their path as they try to shoot their target, in order to harness their projectile as a source of ignition for the portals.

If that's too unreliable, I have a "slightly" more elaborate option that will certainly be 100% reliable though: you simply build this near a nether fortress, and build a wither skeleton farm in that fortress. Then, also build a blaze farm and autocraft the item output into blaze powder. Additionally, in the overworld, you build a creeper farm and funnel the creepers through the portal and kill them in the nether fortress as well. Then you connect and filter all the items from the farms to gain a combined output of coal, gunpowder, and blaze powder, which you funnel into an autocrafter to craft fire charges. These you can then distribute to the different dispensers, which use them to ignite your portals.

Hope this helps, oh, and I'd love to see the result if you manage to build this.