#Tolkien and Lewis started it when Tolkien returned to Oxford.

I'll answer the questions that you mentioned one by one. Unless otherwise specified, the quotes come from *Inside The Lion, The Witch, and The Wardrobe* by James Stuart Bell, Carrie Pyykkonen, and Linda Washington, chapter 5.

**When was it set up?**

>Years later (after working on the *Oxford English Dictionary*), when he returned to Oxford as a professor of Anglo-Saxon (Old English), Tolkien and Lewis founded a writer's group called the Inklings.

According to [Wikipedia](https://en.m.wikipedia.org/wiki/Tolkien), this was in 1925. So the earliest possible year is 1925. But the Wikipedia article on C. S. Lewis claims that they met for the first time in 1926, pushing the possible date farther forwards. 

... 

>This group met weekly (sometimes on Monday or Tuesday mornings, other times on Thursday evenings) during the 1930s and '40s...


**Who were its founding members?**

See my first quote - it looks like Tolkien and Lewis set it up themselves.

>...1930s and' 40s and consisted of Lewis, Tolkien, and Charles Williams: Owed Barfield (Lewis was his daughter's godfather); Warren Lewis; Nevill Coghill (an Oxford professor); John Wain (not to be confused with John Wayne, the American actor famous for westerns - this is John Wain, the English poet and novelist); Gervase Matthews (a lecturer at Oxford); Hugo Dyson (whose talk with Lewis along with Tolkien helped Lewis to believe in God once again); Robert "Humphrey" Havard (another lecturer, who was also Lewis's and Warren's doctor); Lord David Cecil (an Oxford professor); and others, including Tolkien's son Christopher. Some friends and fellow writers like Eric Rucker Eddison (whose novel *The Worm Ouroboros* also was a favorite of Lewis's) and Dorothy Sayers (the Lord Peter Wimsey mystery series) made guest appearances.

...

>- Owen Barfield
- J. A. W. Bennett
- Lord David Cecil
- Nevill Coghill
- Hugo Dyson
- Adam Fox
- Roger Lancelyn Green
- Robert Havard
- C. S. Lewis
- Lewis's elder brother, Warren Lewis
- J. R. R. Tolkien
- Tolkien's son, Christopher Tolkien
- Charles Williams

>  More infrequent visitors included:

>- John David Arnett
- Percy Bates
- James Dundas-Grant
- Jon Fromke
- Colin Hardie
- Gervase Mathew
- R. B. McCallum
- C.E. Stevens
- John Wain
- Charles Leslie Wrenn

>  Guests included:

>- Roy Campbell  
- Eric Rücker Eddison  
<sub>-Wikipedia: [Inklings](https://en.wikipedia.org/wiki/Inklings)</sub>

**Was there any special motivation for it, and how did it grow to its later glory?**

>The Inklings liked hanging out together and hoped to encourage each other in their meetings.

As for why Lewis and Tolkien set up the group in the first place - probably for discussion about the works they were writing, and connecting to other writers. Why do you set up a chess club? For practice, fun, and people. It seems like that would be why they would set up a group like that.