As far the PHP side is concerned it doesn't matter... it's 2 "queries", but one statement... something like this (untested) -- you may need to backtick the date column (reserved keyword!):
SELECT c.storeNum, c.method c.date, c.subject as subject, c.details s.franchisee s.rfc
FROM communications AS c
INNER JOIN stores AS s ON c.storeNum = s.storeNum
INNER JOIN
( SELECT storeNum, MAX(date) AS maxDate FROM communications GROUP BY storeNum ) AS rc ON rc.storeNum = c.storeNum and rc.maxDate = c.date
ORDER BY c.date DESC