I've got a 2007 Camry SE, V-6. Had it since new, and it's had the flare since a few months into owning it. Kentucky built, the first few months of the 'new' model. Happens intermittently, probably more frequent lately. Under hard acceleration, it never does it. 'Average' driving it's there. RPM's go up as described, then grabs 4th. I've learned to 'feather' it, imagining that I am preventing a major meltdown. And, I've got 160,000 miles on the car now. Works fine, still getting good performance out of it. No fix that I know of.. People have tried different things as mentioned. Toyota 'Help'... wasn't. Told that there was a TSP on other models, Solera maybe? But was informed that I didn't have a problem. Dealership no help. Sorta like the Mafia...'What dead body?".
Apparently, 6 months or so after first production, the flare thing went away. If/when it goes... which I somewhat doubt now ( knocking on wood), I'll get a good newer used transmission.. lower mileage, and drive it to 400K. Or that's what nephews are for.... First car 'present'. :)
I pick my battles, this one sucked, and 160K later, its what it is.. Tough to resale. The car is otherwise in great shape, looks and runs great, I got 125,000 miles out of the first set of brake pads.. (Really).