Historian of Modern Spain here. I don't know the total number of Spanish refugees from the Spanish Civil War in Latin America, but I know that in Mexico City alone there were approximately 50,000. The cultural and political effects of the Spanish Civil War and the Spanish emigrant communities on Latin America were quite profound, especially for the history of the Left in Latin America. The Spanish Civil War played a central symbolic role in popular left-wing literature and song- Pablo Neruda writes about it, and there's also Chilean folk singer Rolando Alarcon's famous recording of Spanish Civil War songs.

Mexico plays a particularly strong role in Republican memory of the Spanish Civil War. Mexico was the only country other than the Soviet Union to offer explicit, uncompromising support to the Spanish Republic during the Civil War. They not only accepted Spanish refugees, but refused to recognize the Franco regime for many years. The Spanish Republican Government in exile was headquartered in Mexico City for many years until they returned to France after World War II to help coordinate resistance with the Anti-Francoist movement that was operating underground in Spain.

Spanish emigres hung out with famous artists like Frida Kahlo and Diego Rivera, as you probably already know. These contacts had profound political implications. Most unnervingly, when the Russian revolutionary, Leon Trotsky, lived in Mexico City with Rivera and Kahlo, it was a Spanish agent, Ramon Mercader, employed by the Soviet Union, that was sent to assassinate Trotsky. Mercader's infiltration of the Spanish emigre community facilitated his access to Trotsky.

To be honest, I don't think there is any single book in English that speaks on this topic. All the scholarship I've read about this topic is in Spainsh. So, if you read Spanish, I'll recommend some books:

Balcells, José María y Pérez Bowie, José Antonio (Eds.). El exilio cultural de la Guerra Civil (1936-1939). Universidad de Salamanca, 2001. (Summary of cultural output of Spanish emigrants in exile).

Josep Sanchez Cervello, La segunda república en el exilio (1939-1977). Barcelona: Planeta, 2011. (History of the Republican government in exile.)

Olga Muñoz Carrasco, ed. Perú y la guerra civil española: la voz de los intelectuales. Madrid: Calambur, 2013. (Memory and symbolism of the Spanish Civil War on Peruvian intellectuals.)

Rolando Alarcon, "Viva La Quinta Brigada" Chilean folk rendition of Spanish Civil War song: https://www.youtube.com/watch?v=Fko5fYIBJFU

Street in Mexico City named in honor of the Spanish Civil War emigrant community- Vía del Exilio Español: https://upload.wikimedia.org/wikipedia/commons/3/35/V%C3%ADa_del_Exilio_Espa%C3%B1ol_-_Ciudad_de_M%C3%A9xico.jpg