It varies. You can work it out for any day of the year. It travels from the tropic of cancer to Capricorn. Work out the latitude. How far that latitude is around on a flat earth and divide by 24 hours.
Is sounds as though an experiment could be conducted to see if the sun moves overhead faster during summer in the south along the tropic of capricorn than it does during the summer in the north over the tropic of cancer.
He's (kinda) right, in the heliocentric spherical Earth model, the Sun moves the fastest relative to background star in January and the slowest in July.
Though his model make no attempt explaining why does the Sun move faster in a larger circumference and slower in a smaller circumference.
With the fe model (mono-pole anyway) the sun would be moving along the tropic of capricorn at 2,049mph in December vs 1,204mph along the tropic of cancer in June. That is based on measured distances from the N. pole and the resulting circumferences. I think we all agree the equator is 24,901 miles in circumference, which gives us about 1,040mph for the sun at the equator. Doesn't really add up, I know.
Point is, with the mono-pole model, the sun should be moving noticeably faster along the tropic of capricorn vs the tropic of cancer. An experiment as simple as a stick in the ground and measuring how fast the shadow moves at the appropriate latitudes and times of the year can prove or disprove this.