Heinrich Himmler was one of the very few Nazi leaders who did no worship Adolf Hitler. For a very simple reason – he knew too much about Der Führer from the files he inherited from the political police of the Weimar Republic.
The second one – and for the same reason – was Himmler’s deputy and probably closest associate Reinhard Heydrich (Himmler’s brain is Heydrich there was a common saying in the SS), head of SD, the intelligence department of the SS (he actually delivered these files to Himmler).
Himmler’s attitude to Der Führer was pragmatic – the SS-Reichsfuhrer viewed his boss as but a stepping stone to his ultimate dream: acquiring the absolute power in Germany and building the Ordensstaat 2.0. The SS-Staat. His very own Reich (the Fourth Reich, if you will).
And there was only one way to achieve this objective – wait until the Wehrmacht generals (sooner or later) inevitably depose – and murder – Adolf Hitler and then snatch the power from the hands of hapless generals (who were no match politically to Heinrich Himmler).
Although the SS (SD, Gestapo, etc.) were prohibited from spying on Wehrmacht, its generals were so pathetic in trying to conceal their coup preparations that Himmler knew far in advance about everything they planned to do (it appears that he was also well-informed about the assassination attempts such as one by Georg Elser on November 8th, 1939).
Unfortunately for him, Himmler was not aware that he could defeat the generals only with the supernatural assistance (guidance and energies mostly) of The Black Sun Society (the Wehrmacht was simply way too powerful to be defeated with ordinary, “natural” tools).
Heinrich Himmler (for many reason) did not take supernatural powers seriously and consequently committed the same mistake as his boss in 1920. De-facto severed himself from The Black Sun Society. Hence it is no surprise at all that all his own “coup attempts” (of sorts) came to nothing. Nothing at all.
After the Western Allies successfully landed in Normandy on June 6th, 1944, it became painfully obvious that the war for Nazi Germany was over. The Third Reich lost it.
Himmler intended to use the July 20th, 1944 coup to get rid of his boss, take power in Germany (at the time there was no competition to speak of) and negotiate peace with Western Allies. Offering them an alliance against the “existential Bolshevist threat”.
Unfortunately for him, by that time it was already way too late. After they invaded France, the Allies would agree only on unconditional surrender as they were confident that rather sooner than later, they would defeat Nazi Germany anyway (their aggregate superiority was simply enormous – and thus decisive).
The “anti-Bolshevist alliance” (i.e. joining the Anti-Comintern Pact) made sense for the USA, Britain and their allies in 1941, but not in 1944. Because by the latter date Bolshevism no longer was an existential threat to the Western Civilization (thanks, actually, to German Wehrmacht and Waffen-SS).
Unlike prior to the start of Operation Barbarossa, the Red Army was completely dependent on Allied supplies (i.e. on lend-lease program) for its war effort; so it simply could not fight with the latter.
It lost fat too many men and far too much of its industrial and economic capacity was destroyed. Besides (unlike Nazi Germany), the Soviet Union was totally defenseless before the Allied Air Forces – it simply had neither radars nor fighter aircraft capable of protecting against B-17, B-24 and Lancaster aircraft (let alone the B-29 strategic bomber).
The frontline situation also would have been disastrous – the Red Army was vulnerable even to depleted Luftwaffe (especially the ground attack versions of FW-190 fighter). The Allied Mustangs, Thunderbolts and especially the Typhoons would have decimated everything that the Red Army could field.
And, of course, the Allies had immeasurably better logistics and their overall “troops management system” was far superior to the Soviet one. Oh, and Allied generals and officers were far more competent than their Soviet counterparts (and their soldiers far better trained and skilled fighters).
Hence, there was no reason, no reason at all for the Allies to form an alliance with Nazi Germany – especially under Heinrich Himmler (given the “track record” of both in war crimes and crimes against humanity). None whatsoever.