In 1936 the republican government granted Chiang the Order of Isabella the Catholic.1 Why did they do that?
The Wikipedia article on Chiang is where I got this from.
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TL;DR: Medals were exchanged, but the only that references can be found for happened much later on, and while Chang Kai-sheck did not receive this specific medal he did receive some, and some Chinese nationalists did receive this award. And it was not the Republican government but Franco.
This paper(in Spanish) summarizes the diplomatic relationships.
During the Spanish Civil War there was little information about China; Chiang-Kai-Check was seen as fighting a fascist agression (Japan), so it had the sympathies of the Republican Government, which was not very informed on the internal politics of China. Also, Franco's government recognized Manchukuo on December 2, 1937.
I guess it is somewhat possible that during this period the Republican government issued some award to Chiang Kai-shek, but no reference can be found, and certainly at this time little help could Republican Spain expect from China. And if this had happened, it would be a shocking omission by the paper's author.
Until 1950 Franco's Spain was diplomatically isolated.
Diplomatic relationships were established February 19, 1953, following diplomatic note exchanges since june 1952. The paper lists the similitudes between both leaders: dictators, nationalistic, anticommunists, militaristics (both styled themselves "Generalissimo").
Relations became quickly quite warm, and the paper mentions many amiable mentions an a lot of condecorations being exchanged:
1953: concesión de la Medalla de la Orden del Gran Cordón de la Estrella Brillante a Franco [...] y concesión de la Gran Cruz del Mérito Civil al ministro de Asuntos Exteriores, George K.C. Yeh (Ye Gongchao) y al gobernador de la provincia de Taiwán, Wu.
1953: Franco is awarded the Medal of the Order of the Great Ribbon of the Brilliant Start [...] and award of the Gran Cruz del Mérito Civil to the Foreign Office Minister, George K. C. Yeh (Ye Gongchao) and to the governor of the province of Taiwan, Wu.
1965: [...] visitas a Taiwán del ministro de Industria español, Gregorio López Bravo, y del ministro de Asuntos Exteriores, Fernando María Castiella, junto con la hija de Franco y su marido, y entrevista con Chiang Kai-shek; concesión del Collar de la Orden del Mérito Civil a Chiang Kai-shek y de la Gran Cruz de Isabel la Católica a Mayling Soong (mujer de Chiang Kai-shek), al primer ministro, Yen Chia-kan (Yan Jiagan), y a otros diez altos funcionarios.
1965: visits to Taiwan of the Spanish Minister of Industry, Gregorio López Bravo, and the Foreign Office Minister, Fernando María Castiella, together with Franco's daughter and her husband, and intervieww with Chiang Kai-sheck; award of the Necklace of the Órden del Mérito Civil a Chiang Kai-shek and of the Great Cross of Isabel the Catholic to Mayling Soong (Chiang Kai-shek's wife), to the prime minister, Yen Chia-kan(Yan Jiagan) and other high officers.
And indeed, the WP for the people awarded the higher categories(in Spanish) of this condecoration include some Chinese Nationalist personalities in 1965 (while it does not list twelve of them, it is possible that some of them were awarded lower categories of the condecoration).
I'm not able to find any documentation that this in fact occurred, aside from the unsourced listings on Wikipedia.
If Chiang Kai-Shek did receive the Order, it would have been more likely under Franco. And if there was in fact any connection between Franco and Chiang, it may have been through US Senator and staunch anti-communist Pat McCarran, who did receive the Order. According to the book Franco Sells Spain to America, it was granted to McCarran because he "was so helpful to the ultimately successful cause of achieving normalized US–Spanish relations, gaining for Spain a large US loan and securing the Madrid Pact for US military bases in Spain". McCarran is known to have also received cash payments from both Chiang Kai-Shek and Francisco Franco.