A good way to do it is guaranteeing that no allied troops would be in Spain, it would be enough for the Germans ( because if they invade Spain they cannot conquer all of it before the Brits and Americans start sending troops in mass ... )
That's the only way I see this working at all. Franco does not
want to be at war with Germany, whereas the Allies will be very frustrated with him not offering a second land front against Hitler.
Or third, considering that by this time the Allies have landed in Italy and Italy (those parts of it not under Nazi control anyway) has turned against Mussolini. But the Italian front, while it did to some extent drain the Third Reich and was a valuable training ground for the American forces, was a slow and costly line of advance for the Allies, leading to the natural fortifications of the Alps--clearly a "real" second front was needed.
But if they were to start a buildup of Allied forces in Spain intended to attack Vichy France, Hitler would have little choice but to try and preempt it; the war would move into Spain itself. This would probably be OK with the Americans and British but not a wonderful outcome from their point of view, having to fight their way to the Pyrenees before being able to sweep down from them into France.
Given that the Invasion of Normandy was not possible until a really massive buildup of mostly American forces could accumulate in Britain, Franco entering wholeheartedly into the UN would give the Western Allies a battleground against Hitler where relatively small Anglo-American forces (at this stage more British than American) could start engaging with Germans and gradually build into overwhelming force, assuming they could hold on to strongholds in Spain. But it isn't clear they'd be any farther ahead in the advance to Germany itself come December '44, and it is clear Spain would probably get badly chewed up in the process.
Franco therefore has good reasons, aside from his ideological commitments, to avoid opening the door of Spain to an Allied buildup there. But the question is, how do both Hitler and the Allies react to his offer of limited help against Japan alone?
Hitler at this point is deeply committed on the Eastern Front and Italy, and has to maintain serious forces ready to defend against Allied invasions, not only on the French Atlantic coast but on its Mediterranean shores too and in Scandinavia--Hitler always believed the Allies would in the end attack by invading Norway and he kept forces ready to stop that to the bitter end, long after D-Day mooted that. Can he afford a preemptive attack on Franco on a whim and a suspicion? One thing I have little idea of is just how good intelligence he could rely on regarding what was actually happening in Spain. I'd think that the long association of the Fascists with the Reich would mean the channels of information were relatively good--this means the Allies would be very ill advised to try and sneak in enough force to seriously contend with a large German invasion, let alone strike first at France. And even at this diverging point in the timeline, Franco himself has no hostile intentions toward the Germans and this would probably be true of most Phalangists. Assuming Hitler can reliably verify that in fact there is no buildup of Allied forces happening in Spain, it's in his interest to keep that front neutral, which means his own buildup on the border would also be inhibited to avoid provoking the Allies, aside from his logistical issues. So on the Nazi side I can see this odd "three wars" configuration of Franco's being accepted by them. It's not the like Nazis actually cared what happened to Japan!
However, just how vexed will the Allies be? From their point of view, Spain has stayed neutral thus far because Spain is pretty abjectly dependent on the West--on trade first of all, and second is vulnerable to a determined Allied invasion if they are given cause. One way of looking at Franco's declaration of war on Japan is, it's a free gift of extra forces to be used against Japan and that's well and good enough. But I think they'd constantly be trying to leverage his opening to the West in this one matter to giving them that valuable early land front against Hitler, never mind it would devastate Spain and never mind it might not get them onto German soil any sooner than Overlord would. They don't know that. The Western allies might even take the position that the logistical costs involved in transporting and supporting the Blue Legion to the South Pacific outweigh the value they'd offer as fighting forces once there.
It's evident from the timeline that these naysaying and backbiting grumbles have been overruled, and the Legion is there in the Philippines. Presumably there are enough Nazi spies in Spain still to assure Hitler Spain is not being prepared as an invasion front. The "third war," Spain with the Axis against the USSR, might even be still technically on--I gather Franco did withdraw the Blue Legion from the Eastern Front? He'd better have, or the pressure on him in Allied councils will be that much higher. But on paper I suppose Madrid still hates Moscow and they don't actually get invited to the big summits, not the ones with Soviets present anyway--and Stalin will be that much more suspicious of meetings that don't include his representatives, if Spanish ones show up to them.
I suppose then Franco is on the whole kept at arm's length, agreements between him and the other Allies arrived at via back channels. Even if he were to abjure the war of the Axis on Russia, his neutrality regarding Hitler would be reason enough to keep him sidelined like that anyway, so he might as well stick to his anti-Communist guns--though no one can be sure at this point, of course that would stand him and Spain in good stead half a decade hence and after!
So yes, I suppose the situation Goldstein is (hopefully still?) outlining is plausible enough--a balance of terror keeps Spain neutral in Europe but with this bizarre option of attacking an Axis member on the other side of the world.
I have to say it's a configuration I never imagined possible and therefore worth reading about!