Two on my list that bracket yours are:
394818 -- shipped June '65
&
396602 -- shipped September '65
S&W launched the Chiefs Special in 1950. The earliest ones had the old style thumbpiece, then somewhere within the first 100 came the first flat latch thumbpiece. The flat latches evolved with differing numbers of ridges and slopes till, as S&W historian Roy Jinks said, S&W incorporated a change to replace the flat latch thumbpiece with the original style thumbpiece on February 11, 1966.
S&W only used the flat latches on I and J-frames (one exception is the K-frame Airweight -- with S&W there seems always to be an exception).
Let's see photos of yours, please.