If you want to measure the flare with calipers, then you need to measure around the outside of the male threads or the diameter of the hole. The angle of the flare appears to be 45 degrees, and assuming that your threads are 1+1/16 inch, then the hole is 3/4 inch. That is an unusual size for flexible pipe which is usually 5/8 or 1/2 inch. I searched for a 3/4" female flare to 5/8" male flare, but had no luck. I am sure someone wants to sell such a thing, but I have no idea who.
The tapered threads on iron pipe do NOT create a seal. Pipe sealant is required. I like to the blue stuff, but that is a personal preference. Apply a small measure to the first few threads. Do not get any inside the pipe or it might end up in your appliance and cause problems.
Tighten a gas line until the tightening resistance does not increase. Make sure some threads remain showing or the junction will leak.
Do NOT do this because I am NOT liable for any B.S. in this country filled with inept people that refuse to pay for their own ineptness...
A capable man would turn off the gas outside at the meter and replace the valve. He would also make sure that the pipe in the wall does not turn as he works. He would then remove the uncommon valve and install:
One 3/4 street 90.
One 3/4 x 1/2 reducing bell (bushings are against code because they cannot be tightened one thread at a time).
A short nipple with enough between to attach a wrench without damaging the threads (fully threaded nipples are against code because they cannot be tightened one thread at a time).
Note: Amazon is selling a beautiful stainless 3/4 female x 1/2 male reducer which would perform the conversion in one step.
Lastly, a 1/2" gas shut off valve.
Now you have a standard fitting. Turn the gas back on outside and check that the fast moving pointer is not moving. With a marker, carefully position your head and mark the position of the needle that moves quickly when gas is getting used. Wait 30 minutes, more is better. If the fast moving pointer moved, then you have a problem. There are a million rules involving gas, especially when older appliances exist anywhere in the home. Remember what I told you: Do NOT do replace the valve yourself. You might learn something at a large cost.
Off subject note because the more you tinker, the more you tinker, and the more you learn the better: An abandoned line cannot be shut off with just a valve, it needs a cap. I like reasonable codes for reasonable safety. I think codes reached their reasonable peak around 1980. Since then, we have been moving toward unreasonable fear backed by unreasonable liability. You may have lost the right to repair your car, your computer, and your phone, but at the current time, you still have the right to repair the house that you live in and own.