Why does a Star of David appear at a rally with Francisco Franco?

Q Why does a Star of David appear at a rally with Francisco Franco?

1. Because the symbol was much more ambiguous at the time, and not a one-to-one signifier of "Jewishness".
2. Because Franco had his base in Northern Africa, Morocco, and the symbol represents this early power base, just as the other flags show where his support came from.

Most probably because this is not really a star of David, but a hexagram. As such it has probably less to do with Jews, Zionists or Israel being a part of Franco's movement or even on the guest list for this occasion.

Whether this is an occult symbol, popular with fascists, or a stylised version of an etoile, six pointed star or estrella de seis puntas, the basic pattern is widespread and used in heraldry for cities, where this meeting could have taken place.

Example for six-points (plus: no connection to Islam, despite the crescent) Armañanzas

Example for a Spanish nationalist or Falange fighter, no connection to Jewish symbolism:

(src)

That said, in this case it might simply be a reminder of the glorious origins of the falangist forces of Franco. And that is in North-Africa. The Spanish Protectorate of Morocco sported this type of flag in some variations:

Flag of Morocco in early 20th century
Source: WP List of Moroccan flags

Just like in a French encyclopaedia, copyright 1923.

But compare the apparently argent variant with Spanish Protectorate of Morocco (1912–1956) and

The symbol of armed authority was a hexagram … Starting from the reign of the Sultans Hisham (1790/’92–’97) and Suleyman (1792–1822) the hexagram is uninterruptedly documented on coins until 1956.

But if that sounds still like a tough sell to Catholic Spanish falangistas, either something looking like a Jewish or a Moroccan symbol, then it might be as well recognising a symbol of Mary or [stella maris]13:

Just like the Star of David, the Star of Mary is a Six-Pointed Hexagram

(a) (b)
(a) A 13th century Church in Asturias, Spain known as 'Iglesia de Santa María' (1270 A.D.)

Among the medals and insignia used in connection to the Army of Africa, the Order of the Medhauia seems to stick out:

To reward those very distinguished and notorious facts of Spaniards and Moroccans carried out in the Zone of Morocco entrusted to the Protectorate of Spain.
(a) (b)
_{(a) Rifaat (equivalent to gentleman) Visirial decree of 8 of safar of 1345 —18 August 1926— Award period: 1926–1956 Compose the central part of the badge of an enameled circle, in which the setting Sun is represented, that is to say "The Mogreb", reflected in a blue-green sea. Circumscribed to this circle is a strip, also of enamel and of Prussian blue color, limited by a golden fillet. Everything described above is enclosed in a Solomonic ring. The ribbon on which the decoration hangs is green, with a white central stripe.
On the back, in a circle of white enamel, read the following Arabic inscription: "Muley el Mehdi Ben Ismail Ben Mohamed, glorify him God" Both the Solomonic ring and the ornaments will be silver. It is suspended from the left side of the chest
(b) Sumú-u (equivalent to the Great Cross) Visirial decree of 8 of safar of 1345 —18 August 1926— Award period: 1926–1956 Compose the central part of the badge of an enameled circle, in which the setting Sun is represented, that is to say "The Mogreb", reflected in a blue-green sea. Circumscribed to this circle is a strip, also of enamel and of Prussian blue color, limited by a golden fillet. Everything described above is enclosed in a Solomonic ring. On the back, in a circle of white enamel, read the following Arabic inscription: "Muley el Mehdi Ben Ismail Ben Mohamed, glorify him God" Identical to the previous one and attached to the left side, taking, in addition, a band that crosses the chest from right to left and from whose end the second class badge hangs}

And further campaign militaria offered by wwwmilitariabcncom:

Nationalist Army… Spanish Civil War.
(a) (b)
(a) Army badge Moroccan Army Corps. 92 Division. Nationalist Army. Spanish Civil War.
(b) Collar badge. Supervisor of the Mehala Jalifiana . (Colonial Troops).

And finally, a propaganda poster from that time in colour:

Venus Dictator in Furs. Painting by Paco Ibera

_{Franco in furs like Bette Davis. He wears his Miss España sash in the traditional Spanish colors (as opposed to the red, yellow & purple of the Republican flag) and on his chest is a maltese cross (an order of knighthood perhaps? – this forum leads me to the Grand Cross of the Order of San Fernando). Below the cross is a pin of the symbol of the Falangists. His hand rests on a cane while his other hand holds his hat; a garrison cap with a gold tassel. He tries to strike a regal pose. Franco alone takes up nearly half of the image.}

_{On the lower left is a cartouche with Franco's well known and brief declaration of the end of the Spanish Civil War. In a Roman font it declares in large type "La Guerra ha terminado" (The war is over). There is probably no connection between this and John Lennon's song "War is Over."}

One of the flags in the background is either a pentagram or a hexagram flag of the caliph of Morocco.

Perhaps clearing up some confusion:

WP: Seal of Solomon
The current flag of Morocco, introduced in 1915 (r. Yusef) displays a green pentagram in reference to Solomon.]]The Seal of Solomon (or Ring of Solomon; Arabic: خاتم سليمان‎ Khātam Sulaymān) is the signet ring attributed to King Solomon in medieval Jewish tradition and in Islamic and Western occultism. It was often depicted in either a pentagram or hexagram shape; the latter also known as the Star of David in Jewish tradition.

The difference in modern views about the symbol as such looks sometimes a bit contrived: Understanding the Differences between the Star of David and the Seal of Solomon

But for this application it remains important that the pentagram and hexagram were both used, interchangeably.
Cf Whitney Smith & Ottfried Neubecker: "Wappen und Flaggen aller Nationen", Battenberg: München, 1980 & Georg Eisner: "Vom Hexagramm zum Davidstern" (PDF)

The Seal of Solomon is sometimes a plain pentagram or a hexagram.
H. Henry Spoer: "Arabic Magic Medicinal Bowls", Journal of the American Oriental Society, Vol. 55, No. 3 (Sep., 1935), pp. 237–256.