Stream of Letters to Words
Jelly, 28 bytes

“¤Œæ×¿®¬©¥¤‘Jẋ"$FẋLẊ‘1¦+\Ṭœṗ


A monadic link taking a list and returning a list of lists.

Try it online! (the footer separates the resulting list of lists with spaces)

How?

Uses all the percentages in the distribution rounded to their nearest integer (thus being within the 0.69% allowed thresholds).

“¤Œæ×¿®¬©¥¤‘Jẋ"$FẋLẊ‘1¦+\Ṭœṗ - Link: list (of characters), s
“¤Œæ×¿®¬©¥¤‘                 - code page indexes = [3,19,22,17,11,8,7,6,4,3]
               $             - last two links as a monad:
            J                -   range of length = [1, 2, 3, 4, 5,6,7,8,9,10]
              "              -   zip with:
             ẋ               -     repeat list = [[1,1,1],...,[9,9,9,9],[10,10,10]]
                F            - flatten (into one list of length 100)
                  L          - length of s
                 ẋ           - repeat list (one list of length 100*length(s) with the
                             -              correct distribution of integer lengths)
                   Ẋ         - shuffle
                      ¦      - sparse application of:
                    ‘        -   increment
                     1       -   to indexes: 1 (offset indexes for the partition below)
                        \    - cumulative reduce by:
                       +     -   addition (e.g. [4,4,7,1,...] -&gt; [4,8,15,16,...])
                         Ṭ   - untruth (yield a list with 1s at those indexes (1 indexed)
                          œṗ - partition s at truthy indexes (note: excess ignored)