paso doble as far as I know, is a type of rythm, music, a certain kind of song. It can be danced.
It has nothing but the "Spanishness" in common with flamenco.
Flamenco is not a dance. Flamenco is an art form that encompasses music, poetry and dance in a very visual package. It has been called the most perfect art form, because in it all these aspects create something greater that the mere sum of its ingredients.
There are dozens and dozens of different types of songs "palos", in flamenco. Each has a different rythm, atmosphere, themes, style. Some are danced, some are only sang and played on guitar, some - the most serious ones - were traditionally only sang. Singing is traditionally seen as the soul of flamenco.
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Flamenco derives of a folk art, that developed in Andalucia, that is the southernmost province of Spain. In that area Christians, Jews and Moors (Arabs) coexisted for centuries. The Andalucian gypcies have long held the legacy of flamenco, and are honored as the people that made the syntheses today called flamenco. Flamenco was for a long time the art of persecuted people, as the Christian king and queen who conquered Andalucia from the Moors, started to persecute jews, muslims and gypsies alike in the 15th century.
Flamenco encompasses all the feelings and high- or low points in human existence. Joy, sorrow, loss, despair, love, hope...they are all there.
Flamenco carries old Indian music and dance traditions, as the gypsies - really called "Roma" - most probably (scientists now seem to agree on this) originated from north of India, and for some unknown reason ended up as nomads covering the huge distance from India to North-Africa to Northern Europe. Only in Spain did flamenco develope, although Roma people all over the world are known to make most beautiful music. In many countries they still today are persecuted. During the nazi reign they were persecuted along the jews, and millions and millions Roma people were murdered in the camps.
Flamenco today is an art form, that has stepped out of small cafe's in Andalucian towns, and onto the biggest stages of the western world. You can easily find information on the dance, music, singing, history, stars etc. of flamenco, if you enter "flamenco" in a search machine in internet. Lots of it in English.
Hope to have helped you!