Flamenco guitars might seem similar to traditional Spanish Classical guitars, but due to their iconic play-style they require a much different construction.
Tonewoods
For tonewoods, Flamenco guitars are traditionally made using Spanish Cypress for the back & sides, Cedar neck, Ebony fingerboard and a Spruce (in some occasions Ceder) top. This traditional model is known as the "Blanca", referring to its light and natural colour.
Besides the "Blanca", there is also the "Negra". This model is the same as the "Blanca" construction-wise, but uses darker tonewoods such as cocobolo or indian rosewood. The warmer sound can be heard on many recordings by Paco de Lucía.
In the video underneath, Levi Akkerman will let you hear the difference between a traditional Flamenco Blanca built by Mariano Conde and a Spanish Classical guitar built by Jaroslav Mach. Although the instruments look alike, you can hear the difference in power and attack greatly.
Construction
Because a Flamenco guitarist requires more power and attack in their sound than a Classical guitarist, the construction of these instruments is quite different.
The top is built to be as thin as possible, to get the most vibrations possible. Because the Flamenco guitarist plays using traditional rhythmic accents, an incredibly light double "pickguard" is attached called a Golpeador. For playability, the bridge is lower than on a classical guitar. To prevent the strings from buzzing, the scale length of a Flamenco guitar is often longer and the instrument is stringed with High Tension strings.
The further shape of the instrument is the same, although the Flamenco Guitar can be slightly more shallow and smaller.