2005 Ford Taurus automatic slips from 1st into 2nd gear

Don’t go to AAMCO or any other Chain, such as Cottman, etc. An independent transmission shop is your best bet.

Also, see Tester’s note on a possible Technical Service Bulletin (TSB) on this transmission. A knowledgeable shop might be able to make a repair.

Agree with you that a Flush is not a good idea, but draining the fluid and changing the filter is what should be done every 30,000 to 40,000 miles.