CPL Lee Duncan, the person who found Rin Tin Tin, was not a pilot, he was an aerial observer. He sat in the back of the plane, armed with a machine gun. He was not a trained pilot and could not fly himself.
If flying, you would not be able to hear a dog bark over the wind and motor noise.
When the officer comes to tell Lee and Gaston that they will be joining the 135th (@ 0:16:00) the vehicle in which he arrives has an American flag with 50 stars painted on it. The flag should have had 48 stars in the years of WWI.
The rifles that the "U.S." soldiers carry in the movie are English Number 4, Mark 1, a type introduced to the English Army twenty years later in WW2. U.S. soldiers would be armed with either Model 1903 Springfield or more likely Model 1917 rifles.