Honda and Toyota, especially now, do tend to have fewer incentives, with the main exception being at the end of the model year and calendar year when there are often some cash back and financing offers. Siennas and Odysseys have generally been quite plentiful and had been selling at or below invoice in general, nowhere near the sticker price numbers commanded by the Odyssey many years ago. I find that trade-in values are pretty negotiable to about the same value regardless of brand, especially if you are armed with a few values and perhaps an independent quote or two from something like a Carmax. I find it really depends a lot more on how motivated the salesperson and manager/dealer are, rather than the brand of the dealership.
With the exception of low supply models, I think savvy buyers can get pretty good deals on most popular vehicles. There are plenty of buying services and fixed price dealers to use for negotiations and if you use a service like Carwoo, CarsDirect or one provided by a credit union or warehouse store, through a Zagg affiliate like American Express or Consumer Reports or from more than one of these sources, you can really shop around from your computer to get a pretty good idea on pricing before you do final haggling at the dealer.
I recently went through this on my Highlander Hybrid. Even as supplies dwindled, I had a ton of email/website offers and ended up negotiating a price near invoice and a far better value on my trade-in than my nearest Toyota dealer. I was happy that they actually honored the deal once I arrived, too!
The Flex is a very nice, roomy family vehicle. Another option to consider that is more heavily discounted is the Dodge/Chrysler minivan. They get 17 city, 25 highway and 20 overall (lower on E85). That tends to be just a bit higher than most midsize SUVs with a V6. I rented a 2010 model recently for a week. I found the interior to be somewhat dated it is not quite as fuel efficient or family friendly as the new Honda Odyssey (though the Odyssey really sets the standard there). On the other hand, compared to my Highlander and most midsize SUVs, it is roomier and even more convenient and flexible for family seating and cargo space. Plus, you can get the base trims for under $25k sticker price, even before discounts below invoice price and cash incentives!