I know that flamenco is modular and the improvisation is seen as a manner of combine compas and falsetas, but I want to ask if there is some palo, format, songs that permits the improvisation like jazz. I don't like to put jazz and flamenco in the same sentence, I love both but usually not together. Great crimes have been comitted in the called flamenco fusion, but may be there is an space for improvisation without visiting the dark and tacky side of music.

Rumbas would be the easiest. There are several rumbas chord progressions on YouTube to use as jam tracks or you can record your own ones.

Also, not related but have a listen to Zyryab (not rumbas), I think it could be the closest to a jazz standard but for flamenco (many people has improvised on top of it)