The Mexican Football Federation (FMF) said the appointment of seasoned coach Meza (pictured), who resigned during the qualifiers for the 2002 World Cup after an unhappy spell in charge, was a tribute to his work in club soccer.
"The naming of Meza is a recognition of his career and achievements," said FMF director Nestor de la Torre.
Flores, who has a lot of experience with young players, will then take over for the matches against Chile on September 4 and Colombia five days later as well as a possible third match.
De la Torre said that after the September games, the federation would consider candidates for taking the position on a long-term basis.
Mexico have been without a coach since Javier Aguirre quit following their second round World Cup elimination at the hands of Argentina at the end of last month.
Meza, 62, has won three Mexican championship titles with Toluca and one with Pachuca. He has twice won the CONCACAF Champions Cup with the latter club.
His year in charge of Mexico included a 2-1 World Cup qualifying defeat at home to Costa Rica, the only time they have lost a competitive game at the Azteca stadium.
He quit in 2001 after a 3-1 defeat in Honduras left them in danger of missing out on a place at the following year's World Cup.
Flores, without a club since leaving Guadalajara last year, has also coached Atlas and Leon.
Mexico host Spain at the Azteca on August 11.
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