I have been to both before but not on the same day. My wife and I only have one full afternoon in Florence and I wanted her to see both. Is it possible? If so, what timing would you recommend (start where and for how long)?
You can definitely fit both into an afternoon, especially if you want to concentrate on the highlights in each. Depends how much you know your art and how much you want to spend admiring each work.
I'd start with the Uffizi since it is larger and you might just want to have more time to see the main rooms and artwork. I'd say plan in any case to be there at least 2 - 2 1/2 hours, even if it means lingering a little more in the main rooms and then passing more quickly through those that interest you less.
The Accademia is a smaller museum but it is still full of important artwork. Many just go in and go directly to see the David and that's it, in and out in less than half an hour. I suggest you do the same: go in, turn to the left and then right and get your fill of the David. BUT then head back from where you came in and admire Michelangelo's Prisoners as well right before the David and then return to the first room you came in into the museum. There are marvelous Renaissance paintings in this first room, all so close together that it might be hard to figure where to look. Take one at a time and discover the early Botticelli work as well as Ghirlandaio's work, an amazing artist. If you're musically inclined in any way, there is also a section dedicated to historical musical instruments from this room. You should then head back toward the David again, admire him some more, and then try to ignore him as you also admire the 16th century paintings around him. Then say bye and head toward the other rooms. Each isn't too large, but each has their own historical period and type of masterpieces. The first floor is full of religious, Byzantine "gold" artwork; you decide whether you've had your fill by then and whether to take a look or not. In an hour and a half, or two if you want to linger, you'll also see the highlights in this museum.
All in all, a good afternoon spent immersed in several centuries of Italian art