To seriously attempt to answer this question, I would say that Hugh Wilson and the Merion Committee had preeminent early influence on William Flynn's design philosophy.
Flynn spent a dozen years working with Wilson until the latter's death.
As far as the extent of that philosophy, I think Alan Wilson said it much better than I can;
" We should also be grateful to this committee because they did not as is so often the case deface the landscape. They wisely utilized the natural hazards wherever possible, markedly on the third hole, which Mr. Alison (see below as to identity—W.R.P.) thought the best green he had seen in America, the fourth, fifth, the seventh, the ninth, the eleventh, the sixteenth, the seventeenth, and the eighteenth. We know the bunkering is all artificial but most of it fits into the surrounding landscape so well and has so natural a look that it seems as if many of the bunkers might have been formed by erosion, either wind or water and this of course is the artistic result which should be gotten."
" The most difficult problem for the Construction Committee however, was to try to build a golf course which would be fun for the ordinary golfer to play and at the same time make it really exacting test of golf for the best players. Anyone can build a hard course---all you need is length and severe bunkering—but it may be and often is dull as ditch water for the good player and poison for the poor. Unfortunately, many such courses exist. It is also easy to build a course which will amuse the average player but which affords poor sport for players of ability. The course which offers optional methods of play, which constantly tempts you to take a present risk in hope of securing a future advantage, which encourages fine play and the use of brains as well as brawn and which is a real test for the best and yet is pleasant and interesting for all, is the “Rara avis”, and this most difficult of golfing combinations they succeeded in obtaining, particularly the East course, to a very marked degree. Its continued popularity with the rank and file golfers proves that it is fun for them to play, while the results of three National, numbers of state and lesser championships, Lesley Cup matches, and other competitions, show that as a test of golf it cannot be trifled with by even the world’s best players. It is difficult to say just why this should be so for on analysis the course is not found to be over long, it is not heavily bunkered, it is not tricky, and blind holes are fortunately absent. I think the secret is that it is eternally sound; it is not bunkered to catch weak shots but to encourage fine ones, yet if a man indulges in bad play he is quite sure to find himself paying the penalty."
I think that sums up much of William Flynn's design philosophy and influences quite nicely.
Unless he happened to serve with HH Barker in the 21st artillery regiment in 1915 in Florence, in which case I would argue that Barker snuck into Flynn's pup tent one night and filled Flynn's empty head with the wisdom of the ages.