I've received a feedback from an airport manager that flexible pavement is not recommended for runways within the regions of an extreme hot climates; this is because of the particles of asphalt that generate through the aircraft traffic along the time over runways, in which a potential risk on aircraft engines may occur by vacuuming these particles, and that some airports, accordingly, have replaced the runways' flexible pavement with rigid one. Is that true? Is there any new recent recommendations from ICAO or FAA in this regard??
Answering for ICAO, no there aren't such regulations/recommendations.
All what matters to the regulatory bodies is the ACN-PCN. If seasonal changes affect the PCN, then different PCN's are to be reported.
The bearing strength of a pavement intended for aircraft of apron (ramp) mass greater than 5 700 kg shall be made available using the aircraft classification number — pavement classification number (ACN-PCN) method.
Different PCNs may be reported if the strength of the pavement is subject to significant seasonal variation.
— ICAO Annex 14 Chapter 2
Flexible pavements (asphalt) are actually very common in hot climates, see here: Why are most runways made of asphalt and not concrete?