The history file for redis-cli is hardwired to be
  ~/rediscli_history.

   Many tools allow this to be varied via an environmental
  variable, for example "less" and "mysql" using:

   $LESSHISTFILE
   $MYSQL_HISTFILE

   I would like to suggest that the redis-cli tool allows
  a similar degree of flexibility.

   I'm happy to knock-up a fork/patch if it would be accepted,
  I imagine the main issue is agreeing on the name of the variable
  to be used.  I'd propose "REDISCLI_HISTFILE".

Steve