When it comes to flamenco and chords, there are alternative and ordinary open chords, barre chords and many voicings.
The Spanish cadence
You could use typical open chords when playing in the style of flamenco, especially A minor and E major, which also are used as a cadence. These can in some cases be substituted for barre chords and the G/E chord can be replaced by a regular open G. The Spanish (or Andalusian) cadence include four chords and is often played in A or D minor.
Am - G - F - E or Am - G7 - F - E
Dm - C - Bb - A
The chord called "A" is as you can see similar to a regular A major chord but with a finger on the third fret. You can also alternate between the ordinary A and the flamenco voicing.
The chords in the Spanish cadence can be part of other typical progressions, or forms that is the word used in this music style. Two common progressions, or forms, are por arriba and por medio in which precedes as short cadence:
F - E - F - E - Am - C - F - E (por arriba)
Bb - A - Bb - A - Dm - C - Bb - A (por medio)
These are sometimes prolonged with the "cambio change" as a midle part, resulting in:
F - E - F - E - Am - G - C - Am - G7 - F - E
Bb - A - Bb - A - Dm - C - F - Dm - C7 - Bb - A
Flamenco chords and voicings
Here are additional typical flamenco chords, including voicings.
E and E(b9) can be combined with E followed by a hammer-on on the fourth string!
See the list below for more voicings:
Some chord progressions to try are:
E - Fmaj13/E
Am - G6 - E
Am - E - B7
Am - Em - B7
A - Bb - F - C/G - Bb - A
Am - G/E - Fmaj13/E - E (see tab)
Forms, dances and techniques
In flamenco, the guitarist can play a solo composition or accompanying a dancer. There are several dance styles or forms such as the soleares, the malagueña, the fandango, the farruca and the bulerias. It's common to use long nails which is the only way to accomplish the very common strumming technique rasgueado in an authentic way. A characteristic flamenco guitar technique is the golpe with the ring finger tapping on the wood below the sound hole (which can be heard in the audio above).
Fmaj7 - C7 - Fmaj7 - F6 - F7 - E7
F7 = XX3241
E7 - E13 - E7 - Am
E13 = 020120
A - Bb(#11) - C9 - Bb(#11) - A
Bb(#11) = X13330
E - Am - E - Am
E7 - E7(b9) - Am
E7(b9) = 023130
E - Am - G6 - Fmaj7(#11) - E
G6 = 355400; Fmaj7(#11) = 133200
Combine chords with scales
To enrich the playing with melody lines et cetera you could combine these chords with scales. Two scales frequently used in flamenco are "Por Aribba" and "Por Medio". You can find instructions for these together with more information about chords in this Lesson of Flamenco Guitar.
Spanish chord voicings
One of the alternatives to what have been presented above are these chords, which also can be played mixed with the others.
A simple approach for getting a "Spanish" feel is to play these in this sequence:
E - F - G
Am - G - F - E
You can also combine these with notes from the Am minor scale on the high e-string.
Techniques and rhythms
In flamenco it's fundamental to use proper techniques and congenial rhythms. A useful resource is this lesson: What is Flamenco Guitar? Terms and Techniques You Need to Know.
Here are sound tracks to jam with. The following jam tracks are for flamenco, Spanish and Latin styles and involves only drums.