You could install a crossover switch (the middle one) and then use one channel of the pro as one of the end switches. Or you could use two channels of the pro in interlock mode to function as the crossover switch.
Replacing the center crossover switch with two channels of the pro would look like this:
If you just want to replace one of the existing switches with the pro then the diagram below applies.
In this case on one channel of the pro the common would be say for the left switch the "hot" wire with the NO and NC connected to the other two wires. Replacing the right switch the common would go to the bulb center pin with the NO and NC connecting to the other two wires.
Not sure what you mean by "on" with a 3 way switch. The common always connects to one contact or the other. In the case of a relay when it isn't energized the NC is connected to the common and when energized the NO is to the common.
To replace the left switch with one channel of the pro. The hot wire goes to the common on the relay. The top red wire connects to the NC. The bottom black wire goes to the NO.
With this connection current flows exactly like the diagram when the right switch common is connected to the top red wire. Energizing the relay OR switching the physical switch will turn off the light.
All I can do is provide the diagrams. If you have two existing 3-way switches and wish to keep both of them then use the diagram above to add a 4-way crossover switch between them using two channels of the Sonoff in interlock mode. It will work if you wire it correctly.
Keep in mind that the Sonoff requires an always hot wire and a neutral to power it. It cannot be powered from either of the two "traveler" wires. One of the two channels used has to be energized at all times. Having both channels d-energized will not work. For example if you use channel 1 and 2 then you only switch on ch 1 or 2 in the app with ch 3 and 4 never turned on.