Something I've come to believe over the years is that it's easy to criticize, but more difficult to suggest viable alternatives. My last post was a critique of StarCraft II: Heart of the Swarm; this post will be how I would have handled the storyline if I were writing it.
(For the record, all I know about the story comes from cinematics and TVTropes. All errors are my own.)
*The beginning of the campaign is awesome as it is. The TVTropes "Funny" page references a couple really amusing exchanges between Jim Raynor and Sarah Kerrigan (one pertaining to zerglings and the other to their different types of hair) that are really clever. And Arcturus Mengsk attacking the Hyperion even when Matt Horner has broadcast that his son is aboard does a good job showing just how vindictive Daddy Mengsk is--Valerian says, "My father will take any piece off the chessboard to get the queen" or something to that effect. And when Kerrigan thinks Raynor is dead, that and its consequences are well-done.
My only beef is that everyone on the bridge seems too relaxed when Kerrigan rumbles in during the escape from the Umojan facility. The core of Raynor's Raiders were people who deserted Mengsk over Kerrigan's betrayal in the first game, but she's been the terrible overlord of the Zerg for the last five years, the Zerg they'd fought in a battle from hell only a few weeks ago (I don't know the length of time the novel StarCraft II: Flashpoint covers between Starcraft II: Wings of Liberty and Heart of the Swarm). I would expect some more mistrust, especially given how in Flashpoint, Kerrigan accidentally killed one of the Raiders while fighting the Dominion.
*However, I would have avoided the return to Zerus, the whole goofy "Primal Zerg" story, and Kerrigan voluntarily re-infesting herself. Given how Zeratul had returned to Aiur at some point prior to Wings of Liberty and communed with the shade of Tassadar near the Overmind's corpse, it would be better if he had told Kerrigan she had to go to Aiur to find out what she needs to know to face the Dark Voice, the undead Xel'Naga Amon. That'd also set up a fight with the Protoss, returning en masse to reclaim their Zerg-ravaged homeworld. They could assume Kerrigan is there to reinforce the Zerg occupation forces or simply refuse to believe that she's there with Zeratul's blessing and try to kill her to avenge Aldaris and Raszagal from Brood War. If there's some need to remove the "taint" of the Dark Voice from Kerrigan herself (dubious as other than the hair she's not Zerg anymore and could control the Zerg even as a full human in the back-story), this could be done via some psychic thing with the dead Overmind and the ghostly Tassadar rather than reinfestation.
*The confrontation with Samir Duran can come as it did in the game. That was fun. How Kerrigan could win it without being reinfested (she ultimately used her extra Zerg limbs to kill Duran even after he had impaled her on some kind of energy blade) I'm not sure. If she's not reinfested, Duran can't momentarily shock her by shifting into her human form, so perhaps he can simply use the fact he's got thousands of years of combat experience (and non-"Primal" Kerrigan isn't as powerful) to knock her around for a bit before she manages to turn the tables.
*The rescue of Raynor from the prison and the war with the Dominion can go roughly the same as before. Raynor will not abandon her because she hasn't voluntarily re-infested, but if the "Zerg only" dynamic needs to be preserved, maybe the Raiders (and Valerian) mount a big diversionary attack somewhere else, allowing for Kerrigan to destroy the hybrid-creation facilities and march on Korhal. This is where we could work in my idea from a couple years back about Kerrigan finding Raynor's son in the Dominion Ghost program. Or, if the Ghost Academy doesn't get destroyed, maybe she finds him being used in the hybrid-creation program somehow. He is a psychic, after all.
*Like in the game, everyone comes together for the final assault on Korhal. Maybe the remnants of the UED expeditionary force can join with the Raiders for the human part of the attack, acknowledging the UED's remaining presence in the sector. And since how some of the Zerg campaign missions mirror Terran missions from Wings of Liberty (according to what I've read), Mengsk's recapture of the Xel'Naga artifact allows for a reversed version of the last Terran missions from Wings of Liberty. The artifact could be used to blunt individual Zerg attacks or used to wipe out massive numbers of Zerg a la the end of Wings of Liberty, forcing the human troops to bear more of the burden.
Given how much of Kerrigan's "I'm not a monster anymore" comes from her desire to avoid civilian deaths even if it puts her at a military disadvantage, maybe they send Valerian to negotiate Arcturus's surrender rather than face an extended bloodbath on Korhal. They might think him being the Dominion heir will mean something to the old man, or Valerian himself might volunteer out of some sense of duty. Instead Arcturus takes Valerian hostage to try to force Raynor and Kerrigan to surrender or something like that. Raynor and Kerrigan try to stage a commando mission (maybe just the two of them, like at the beginning of the game) to rescue Valerian and it all goes south. Valerian is killed (perhaps by accident) and Arcturus flees with his most psychotic loyalists to the Dark Voice, perhaps thinking that he'll be able to take Duran's place as the Dark Voice's Antichrist.
Although the later stages of the campaign are more hopeful and sunny than canon (no reinfestation and breach with Raynor), it all goes to hell at the end. Valerian would have represented a chance to hold the Terran Dominion together after Mengsk's overthrow--now there's only Raynor, a known collaborator with two different species of aliens, and Kerrigan, who most of human space views as a monster. And thanks to Kerrigan mistakenly thinking Raynor was dead, there's no respected General Horace Warfield to back them up.
Although the Dark Voice will not be able to use the Zerg to exterminate the Terrans and Protoss like in Zeratul's vision, instead human space will be disunited and at least parts of the splintered Dominion might be willing to ally with the Dark Voice instead of a pair of (to them) species-traitors. And with Mengsk taking the Xel'Naga artifact to the Dark Voice, the enemy now has a potential weapon of genocide against both the Zerg and apparently the Protoss.
(Got to give credit where it's due. The idea that Mengsk might ally with the Dark Voice and the Terrans would be "meat shields" for the hybrids instead of the Zerg during the coming uber-war might have come from someone else on Battle.net discussions.)