There are two parts to your problem and you need to distinguish them to figure out where to look.
Flipper button switch (opto board) recognition.
Test the flipper power side by running the flipper test (T.12) in the tests available. Make sure you have high voltage available by closing the interlock switch in the coin door. If the flippers pass the power test then there's nothing wrong on the power side of your issue (and nothing wrong with the fuses or transistors on the Fliptronic II board).
Test the flipper button switches (opto board) by running the switch test (T.1) and pressing the buttons. I think you've already done this and the upper flipper buttons do NOT register. These are F2, F4, F6 and F8. It also looks like you've verified the voltages for the optos and the optos appear to drop to 0V when interrupted.
To differentiate between the optos and the Fliptronic II board short the pins on the board at J905. Enter switch test (T.1).
F2 - short pin 1 to pin 6.
F4 - short pin 2 to pin 6.
F6 - short pin 3 to pin 6.
F8 - short pin 5 to pin 6.
If shorting the pins does not register the switches then your problem is on the Fliptronic II board. It could be the LM339 or the 74HCT244 or both of them. The LM339 in question is U6 (connects to J905) and the 74HCT244 is U5. You can statically test these in circuit to see if there is a pin that is shorted or open.
I've had this problem on a Fliptronic II board twice before. Once was both the 74HCT244 and LM339. The other time it was the 74HCT244.
I agree with Vireland. If you replace the ICs put a socket in the board first.