If.Rey's Falcon gets.the extra hit.on basic

No, the assist is when an ally uses their basic attack, which the falcon will only do once (though it may “hit” multiple times). The wording they’d use would be “attacks again”, so if you use first order Tie Fighter and it attacked twice with its basic, then RP would have 2 chances to assist. This is also true for counters. For example, if rey’s Falcon attacked slave 1 while it had retribution, slave 1 would only counter once, no matter how many times Rey hit it (but it would counter twice if FOTF double tapped).