You measure it in 2 ways.
First, fill the joint to flush condition. Then you calculate the effective weld size as you see in D1.1 Figure 3.3.
The 2nd way, fit-up a mock-up joint to exactly what you will be welding, weld as you plan on doing in production, then cut it to reveal the weld cross section. You can measure the throat from that.
It would seem that filling in a flare-bevel joint would provide more weld metal than a fillet weld will. And that is true, partially. The problem is that the throat, or thinnest part of the weld, might not even equal what you get with a fillet. In effect, you get a wide weld, but maybe not as thick a weld.
Since a fillet weld was detailed for what is actually a flare bevel, you might want to kick it back to the engineer for clarification. Then you don't have to figure anything out.