Q: Is there any valid basis for this claim that German Emperor Wilhelm II and the Hohenzollern family had Jewish blood?
No.
Title of the pamphlet: "1888-1918. Eine genealogisch-rassengeschichtliche Aufklärung zur Warnung für die Zukunft - ein packender Kommentar zu den Semi-Alliancen im besonderen und semi-gothaischen Erkenntnissen im allgemeinen."
translated: 1888-1918: A genealogical-racial-historical enlightenment as a warning for the future – a gripping commentary on the semi-alliances in particular and semi-Gothaic insights in general."
How nice! A convenient explanation for the downfall of the German Empire, since the Kaiser was Jewish! Well, a semi-semite, as allegedly he was only half (or whatever ratio).
This dreck pamphlet was published by Franz Eher Nachfolger Verlag. That was the NSDAP Nazi publisher, property of the party. It is to be expected to contain plain antisemitism, since it was specialised in antisemitic stuff? But it was not specialised in publishing accurate information.
In this case
Pickl's works, too are a idiosyncratic amalgam of unreliable information and pure invective, anecdotal digressions and pseudo-scientific sermons.
–– Joachim Kalka: "Gaslight: Lantern Slides from the Nineteenth Century" NYRoB, 2017. (p)
If anyone is interested in this "genealogy" or more like fantasy tree, it would be better for any invested money: instead to buy this antique book to go for
In short: "yeah, sure. Wilhelm had Jewish blood, and was as the title suggests a semitic imperator"; according to a paranoid antisemite who presents his outlandish claims.
You don't really need a family tree for that. That is easily 'verifiable', as it was after 1918 Pickl's lifework assignment to prove that the entire European nobility was descended from Jewish ancestors. According to him, or any antisemite, this then "explains everything", but seems to have been like a rather overambitious undertaking compared to real numbers. Or simply a paranoid and hate-fuelled lie.
This book is online in forums censored by search engines. Perhaps for being a little bit too racist overall and for promoting nazism and antisemitism. But not even the bigger conspiracy wikis use it as a source. Equally Pickl's collaborator Stauff isn't into this allegation in his later publication, to the contrary, depicting the Hohenzollern as 'ur-German family under constant onslaught of world-jewishness,' etc.
However, a hint may suffice.
The allegation that the final aim of this Secret Government is the establishment of a universal Jewish dominion under a Prince of the House of David is a curious muddle of eschatology and politics. With much better reason the early Anabaptists said virtually the same thing of the Roman Catholic Church, and, indeed, on the Morning Post plan of campaign, it might be retorted on all the great Churches. With the Jews it has no more to do with practical politics than the analogous hopes of pious Christendom. The Morning Post, however, does not stand alone in its error.
A curious variant of it is found in recent German Antisemitica. The World Unrest is there pictured as due to a conspiracy of Jewry and the British Empire, based on the Anglo-Israelitish theory that the British people are the Lost Tribes and the Royal House of Windsor the authentic seed of David. Accordingly, Britons and Jews together are accused of having plotted the late war in order to fulfil the Messianic prophecies in the person of King George.7 Les grands esprits se rencontrent!
See Wichtl and Meister op. cit. A peculiarly crazy statement of this theory, illustrated by an obscene chart pedigree of Queen Victoria, will be found in Semi-Imperator (Munich, 1919). Cf. Proceedings of the British Israel World Federation Congress, July 5-10, 1920.
–– Lucien Wolf: "The myth of the Jewish menace in world affairs or, The truth about the forged protocols of the elders of Zion", Macmillan: New York, Boston, 1921.
Having this tree in front of me, this description by Wolf is accurate:
Pickl really traces this all back to legendary Kind David of the Old Testament, whose bloodline then goes after 70 AD(!) to the British Isles, "infecting all Scottish, Irish and English Kings", most prominently "Jacob I, rumoured to be a 'Religionsjude'" (on top?). Note that he uses Tea Tephi as the named link, but dates her to 75AD!
The real chart starts then George III (direct line to David)) and gives Queen Victoria two 'Jewish' parents (without much explanation in the chart). The same is repeated for Wilhelm's mother Vicki, who gets not only Victoria's Jewishness but also from Albert, who again gets this 'blood' exclusively froma gratitious donation by Pickl.
If that still isn't enough, Worldcat lists a few libraries interested in keeping it around.
But it's not of much use to just check for Wilhelm's ancestry. The official names of his ancestors are exact on Pickl's fold-out map.
They look exactly like this (well, in fraktur, and a few star of David ornaments…):

Pickl only introduces disputed, unproven or meanwhile long refuted paternity allegations from several levels of his mother's ancestry – in addition to all English kings being 'Jewish' anyway.
Note that Pickl emphasises that even if all of King David's descendants would have out-married non-Jews, he still would count them as 'full Jews, without hesitation'.
That is a singularity in absurdity.
A note on "Jewish blood":
Going back to Ferdinand II of Aragon (1479–1516) and Elizabeth of York (1466-1503) in search of "Jewish blood" for Wilhelm II (1859–1941) seems excessive for timeline considerations alone. Not even Nuremberg Race laws go back that far.
And how are Ferdinand and Elizabeth Jewish? Just by having had "apparently Jewish origins"? Is there even any proof for that? So far back in the timeline we start to quickly approach 'every European being related to every other one'. Even if not out of conspiratorial brack, it becomes senseless pretty fast.