In An Instinct for Dragons by anthropologist David E. Jones points out that dragons are pretty much universal in human folklore. He catalogs dragon legends from multiple cultures and hypothesizes that many aspects of the so called dragons are universal.
Dragons have been a recurring theme in Human Mythology for countless generations. They are very ancient tales, and also very wide spread and trans cultural. Throughout Europe and the far east we have dragon legends.
He argues that even the Eskimo's have reptilian dragons in their folk lore, even though the climate in which they reside does not harbor any modern day members of the reptilian realm and they had never seen an actual reptile upon which to base their legends. Tizheruk is one of the Eskimo Dragon legends, they are large, snake-like sea creatures that are believed to roam Alaska's waters. They are described as up to 15 feet long with a 7 foot head and a tail ending in a flipper, similar to loch ness type creatures, but not as pleasantly disposed. Other Eskimo / Inuits legends tell of the kikituk, a seagoing reptile capable of walking along the shore to hunt . Bone carvings of these gigantic four-legged reptiles confronting men as well as caribou were cataloged in 1897. 
Jones speculates that over many millennia of evolution, members of any species - human beings inclusive - will develop an instinctive fear and respect of their natural enemies, the predators that seek to devour them. He also presents possible sociological explanations for why such imagery is perceived differently at various stages of cultural development and in different cultures.
Dragons and Dinosaurs in the Bible
Judaeo Christian lore mentions dragons and dinosaur like creatures in the Old Testament scriptures and assigns a malevolent nature.
In Isaiah 27:1 "In that day the Lord with his hard and great and strong sword will punish Leviathan the fleeing serpent, Leviathan the twisting serpent, and he will slay the dragon that is in the sea."
The New testament Book of Revelations might well be building on Old Testament lore in its Dragon Narratives
Revelation 12:1 " A great sign appeared in heaven: a woman clothed with the sun, with the moon under her feet and a crown of twelve stars on her head. She was pregnant and cried out in pain as she was about to give birth. Then another sign appeared in heaven: an enormous red dragon with seven heads and ten horns and seven crowns on its heads." 12:7 "Then war broke out in heaven. Michael and his angels fought against the dragon, and the dragon and his angels fought back." 12:9 "The great dragon was hurled down, that ancient serpent called the devil, or Satan, who leads the whole world astray. He was hurled to the earth, and his angels with him." Revelation 20:2 "He seized the dragon, that ancient serpent, who is the devil, or Satan, and bound him for a thousand years."
It is quite possible that the Judaeo-Christian myths draw upon older Sumerian and Egyptian legends. An Sumerian myth tells of a creature called 'Tiamat' a horned 4 legged serpent, and also a legless serpent 'Zu' both of which have malevolent natures. 
Dinosaurs and Dragons in World Cultures
Egyptian creation myths describe the serpent like dragon Apep who is somewhat like the serpent of Eden. He is the spirit of evil, chaos and darkness and depicted as a Giant Serpent.  Babylonians, Hittites and Persians all had their own Dragon legends as well.
Ancient Romans used the Dragon as a symbol of strength for their military in much the same way America uses the Bald Eagle and Russia the Bear. In medieval England slaying a dragon could not only get you laid by a damsel in distress it also got you Knighthood.
Modern Dinosaurs and Anthropological Evidence
Anthropology and archaeology is the study of human cultures while Paleontology is the study of the evolution of plants and animals.
There is a trove of paleontological evidence to prove that Dinosaurs existed, there is a minuscule amount to prove that Humans and Dinosaurs Co-existed.
In Africa the Dragons are serpent-like and at times two legged as opposed to the predominantly 4 legged leviathans of Eurasian Myths. At present Mokele-Mbembe a dinosaur like cryptid is said to still dwell in the Congo jungle. Some Photographs from a 1970s expedition survive, while others including a video are lost, misplaced or destroyed 
The Australian Aborigines, isolated from the bulk of humanity also have their own dragon legends such as the rainbow serpent and the bunyip, which is/was said to make its habitat in ponds and streams. Aborigines also have traditions of massive reptiles that lived in the swamps, ate plants, had a small head which sat at the end of a very long and narrow neck. Its massive body was carried on 4 legs, which were followed by a long pointed tail . A near perfect description of a class of dinosaurs science has labeled sauropods See: Sea Serpents Lake Monsters and Dinosaurs. Another Aboriginal legend tells of the 'whowie' a dragon like creature which is somewhat reminiscent of the Egyptian Dragon God Apep and ties in with their Creation Myths - called the "Dream-Time" by the Native Australians. 
In Hawaii the legends tell of a dragon called a mo'o which ranks among Polynesians most mysterious mythical creatures. They were considered "Ghost Gods" of the ancient Hawaiians. New Zealanders used similar names for their Dragon Gods but pronounced it with a 'K' - the dragons became the Mo-ko. 
Native American legends are rife with tales of Dragons starting with the feathered serpent - god of the Mayans, and ranging both North and South , such as the Angont, a Canadian native legend of a large predatory reptile found in desolate places.
Tales of Giant flying dinosaurs are also wide spread and credible - Indians of the Pacific Northwest have tales of thunderbirds that would carry off whales away into their Mountain nests. The Twana Indians who were in control of the Hood Canal Region to the end of the 1850s, said their hunters sometimes found nests of Thunderbirds in the mountains and they also found whale bones. The Quinnault another tribe of the area had a story of a whale found thrashing about on a mountain with its dorsal fin missing. See - Thunderbird Legends
Other tales of flying dinosaur like birds come from Not only North America, but Indonesia in the South Pacific. In New Guinea many local people in some extremely rural communities carry on ancient local languages and traditions which tell of a very large and ominous creature that glows in the dark as it sails through the night skies. Although it is referred to by various names, the most common are Kor and ropen. See - Living Pterosaurs, Pterodactyls
That Dragon tales appear throughout recorded history and in nearly every culture is undeniable. The origins of these tales are muted by time. Some may well be simply fairy tales but many may also be primal memories of a time when Dragons and Men coexisted. As per conventional Modern science man and dinosaur / dragon never co-existed - accumulative mounting evidence seems to indicate that perhaps this hypothesis is in dire need of re-evaluation.
In fact some evidence seems to indicate that not only did we co-exist with these reptilian monstrosities in the past but that scattered remnants of the Dinosaur Realm lingers on till this very day.
There is an ancient Roman town in the Golan Heights by Israel that harbored a Synagogue known as Umm El-Kanatir [mother of the arches]. The Jews occupied it from circa 400 AD till it was turned to ruins by an Earthquake in 749 AD.
Excavations in 2003 uncovered a stone carving that seems to depicts two Dinosaurs attacking a horse. The most common intertretation is that one Dinosaur was chasing the horse while another would hide and lunge out and to ambush the prey.
1. Dragons, a Brief History Long in Miles NY Times By DONALD G. McNEIL Jr. April 29, 2003
2. Enuma Elish: The Babylonian Creation Epic
3. Egyptian Gods: The Gods and Goddesses of Ancient Egypt
4. Evil in Our Midst: A Chilling Glimpse of Our Most Feared and Frightening Demons David E. Jones 9/2001 Pgs. 26 - 31
5. Reclaiming the Loch Ness Monster
6. Legends of Gods and Ghosts Collected and Translated from the Hawaiian W. D. Westervelt 7/2016 Pg. 235
7. Bunyips: Australia's folklore of fear Robert Holden 6/2004 Pg. 118