I don't know what you are calling flared fittings other than the black plastic nuts that screw onto the back of the valve. They are Culligan parts and are installed on the soldered copper. All brands of valves have their own proprietary plumbing fittings. So you unsolder the copper and solder on the new fittings for your brand and model valve. Or, use brass or plastic push or compression type fittings instead of soldering.
BTW, you can buy a soldering kit from the big box stores or online for $40-$75. And you get to keep it when finished. You can learn to solder with about 30 minutes of practice. To do that you can find free videos and instructions online.
Flexible lines like Falcon SS are difficult to get to fit well with your loop plumbing because you can't move it without tearing the wall apart. And they don't hold the softener from being moved if bumped.