Seems like these flights don't hit sunset, so he should be OK, no?
He davens Thursday shacharis before departure and Thursday mincha after landing.
He's leaving on 40 omer and arriving on 40 omer.

JAL table:

These flights fly against the sun. This means there will be day-night-day in quicker succession than usual. The only reason you are landing at JFK on same weekday is due to crossing the dateline. Thus, were you to take such a flight, there would be night along with Maariv and Sefiras Haomer mid-flight. When arriving in JFK, your Sefirah count would be one day ahead of the locals.
I can’t account for the Zmanim chart you posted above. Perhaps it is assuming a polar route. But recently flights are not flying that North (perhaps due to Russia/Ukraine ban). Based on recent flight paths you would definitely have night in the middle.
JAL #6 recent flight paths:
https://flightaware.com/live/flight/JAL6ANA #110 recent flight paths:
https://flightaware.com/live/flight/JAL6[PS. Even if the flight did fly in the Arctic Circle, the absence of dark does not necessarily mean there is no night. But that's a separate discussion.]