you should be able to get flatwound from davis. Thats where i got mine,
Flatwound on a solid body wont give a good tone imho. The flatwound is only the E A D and G strings. The high E and B strings are the same as normal electric.
The characteristic of flatwound string is rather dull . It dont resonate as much as a normal nickel wound electric guitar string.
The tone characteristic of the arch top is maninly due to the hollow body structure. Putting the flatwound on a solidbody might not sound too good. You might find that your tone is quite "dead" with the flatwound on a solidbody.
To get a jazzy fat tone on a solidbody, you can use thicker gauge strings with a wound G, Low E at .56-.58 wheras high E at .012 or .013. Best with neck humbucker and tone knob turn down to 5 or below. Amp setting, turn down treble, boost the mid and bass up.
If you want to use thicker gauge strings(at standard tuning) , you will definitely have to adjust the truss rod. The tension will be very great, but its still possible to do it. If you are using a floyd rose equipped guitar, forget bout it, its not easy to do it. But if using fixed bridge, it will be much much more easier to adjust the guitar for thicker strings