The speaking very fast (with no spaces or punctuation) was what tripped my mind. The creature is a "bunjee", a mammoth-like creature with suction-cup feet, and could inflate its trunk to fly.
The creature doesn't time travel on its own, but the protagonists travel back in time to rescue their father from a prehistoric era. I don't recall if the bunjee comes back to the present with them or not though.
The book is called "The Bunjee Venture" by Stan McMurtry.
Goodreads link: https://www.goodreads.com/book/show/412535.The_Bunjee_Venture
Edited to add:
I found the name of the book by searching for "childrens novel Bunjee", since I recognised the description of a flying elephant-like creature who spoke fast (with no punctuation or spaces)