Meaning of the Colours
It is fairly clear the the colours have not been arrived at from any symbolism such as "red for the bullfighters' blood on the sand of the bullfighting ring" or "red for the blood shed by Spaniards and yellow for the Spanish sun". The more prosaic answer is probably that the colours originated from Spanish kingdoms' coats-of-arms. Castile has a yellow castle on a red field, Leon has a purple —sometimes dark red— lion carrying a yellow crown on a white field, Catalonia/Aragon has four red vertical pallets on a yellow field, Navarre a yellow chain on a red field. In other words they were probably chosen when the flag evolved in 1785 as common colours to house the coat of arms that was to be placed on the flag.
The colours chosen in the 1785 contest were consistant among all the 12 designs Red, yellow, white and blue were preferred to other colours. It may have been that long distance recognition capability played a role as important as tradition, given that the brief was to develop a war flag that could be recognised as different from other nations during sea battles.
There is a specification of the colours to be used for the Spanish flag in the Spanish legislation. This is not Pantone but the CIELAB system. The Boletín Oficial del Estado states:
Color Denominacion color Tono H* en ° Croma C* Claridad L*
Rojo Rojo bandera 35.0 70.0 37.0
Amarillo Amarillo gualda bandera 85.0 95.0 80.0
The International System CIE 1.931 is also mentioned:
Denominacion color Y x y
Rojo bandera 9.5 0.614 0.320
Amarillo gualda bandera 56.7 0.488 0.469
The Flag of Spain