√KEL was established as the root for “flow” very early in Tolkien’s Elvish languages, also with the variant vocalic extension √KELU. ᴱ√KELE appeared in the Qenya Lexicon of the 1910s glossed “flow, run” and also “ooze, trickle”, though the latter sense did not appear in later writing (QL/46). It also had a variant ᴱ√KELU elsewhere compared to ᴱ√QEL+U of similar meaning (QL/75). It had derivatives in both Qenya and Gnomish such as ᴱQ. kelu- “flow”, G. celu- “trickle” and ᴱQ. kelu(me)/G. celu “stream” (QL/75; GL/25).
The root ᴹ√KEL reappeared in The Etymologies of the 1930s where it seems to have an added connotation of “flow downwards”, given its gloss “go, run (especially of water), flow away downhill” (Ety/KEL). This more specific meaning to the root continued to appear in later writings, with glosses such as 1930s “flow, flow away, run (of rivers)” (PE18/58), 1940s “run away especially downwards or at end” (PE22/114), 1950s “go away, flow away or flow down (of water)” (PE18/103), and 1960s “flow (down)” (PE17/157). The u-extension ✶kelu with the (continuative?) sense “flow, well up” remained common throughout all these periods as well (PE18/86; PE22/98, 133, 135).
Starting with The Etymologies of the 1930s, Tolkien compared this root with etymological variants √KWEL “fade (away), die away, grow faint” and √KYEL “come to an end, cease, run out” (Ety/KWEL, KYEL; PE18/58, 103), and indeed Tolkien used it as one of his basic examples of such etymological variations:
> There existed in Quenderin 1. √KEL “flow, flow away, run (of rivers)”. Of this simple base, since the initial variation is possible, while the sundóma is the same 2. √KJEL “cease, come to an end”, and 3. √KWEL “fade, die away, grow faint” may be regarded as differentiated variants (second version of Tengwesta Qenderinwa, TQ2, circa 1950, PE18/103).
A similar note appeared in the first version of Tengwesta Qenderinwa (TQ1) from the 1930s (PE18/58). Likewise ✶kelu was one of his main examples of variant vocalic extensions:
> This “variant extension” always had the form i or u. It appears in many cases where its original function is no longer discoverable, if indeed that was more than to serve as a euphonic connecting link to affixes. But the added element [u] often appears as a differentiator as in kel¹-u beside kel², and some old verbs have a fixed u as the end of their base (TQ2, PE18/86).
In the Quendi and Eldar essay of 1959-60, it seems that √KYEL “end” was replaced by √TEL “close, end, come to an end” (WJ/411) as indicated by the replacement of 1930s ᴹQ. tyelma “ending” (LR/72) by later Q. telma “conclusion” (WJ/411). In a 1967 note the etymological variant √KYEL seems to have been assigned a new meaning “go down slowly”, which served as the basis for Q. tyellë “grade, a step in a stairway or ladder” (PE17/157).
To summarize, the base root √KEL meant “flow (down)” for pretty much all of Tolkien’s life, usually used with a variant vocalic extension √KELU, and starting in the 1930s it had etymological variants √KWEL and √KYEL, with √KWEL always meaning “fade (away), die” and √KYEL meaning “cease, end” from the 1930s to 40s, but changing to “go down slowly” sometime between the 1950 and 1967 (but probably before the 1st edition of LotR), with “end” being reassigned to √TEL by 1960. See the entry on √TEL for further discussion of those developments.
A root appearing in an undated note from around 1968 as part of an explanation for the tree-name S. lebethron, given as {√RON >>} √RUN “rub, grind, smooth, polish”, with a derivatives Q. runda “smooth, polished” and [deleted] ron “smoothed by polishing”, probably Sindarin (PE17/89).
The Etymologies of the 1930s instead had the root ᴹ√RUN “flat of hand or sole of foot” with derivatives like ᴹQ. runya/N. rhein “footprint”, and also as the basis for the final element of ᴹQ. tallune/N. tellen “sole of foot” (Ety/RUN). It’s conceivable the two iterations of the root are related based on the “smoothness” of the hand or foot.