if you have a promo eevee on your bench with a mysterious fossil active and
you evolve mf into aerodactyl do you use chain reaction to search for an
eeveelution or does aerodactyls power cancel it?

You absolutely can.  Aerodactyl's power will prevent all evolving the normal ways.  Eevee's Chain Reaction, Magikarp's Rapid Evoltion, and any card worded like that gets around the regular methods of evolution, thus being unaffected by Aerodactyl.