No, there's no connection between the two groups.
As you noted, the Masonic Rainbow Girls were founded in Oklahoma in
1922. See: International Order of the Rainbow for Girls: History.
Masonic Rainbow Girls founder W. Mark Sexson was a minister of the
Christian (Disciples) Church. He had no affiliation with the
Assemblies of God.
"Rainbows" at the Assemblies of God are part of that church's
See: Missionettes: Rainbows Club
The Missionettes program was created in the 1950s, and has no
connection to the Masonic Rainbow Girls.
"History of Missionettes
Early in the 1950s, women began to see a need for a program to teach
missions to young women and to prepare them for future involvement in
Women?s Ministries. The national Women?s Ministries Department
developed the Missionettes program in response to this need.
The first Missionettes club was officially chartered in January 1956.
Since then, Missionettes clubs continue to be organized across the
United States and in many foreign countries. Along the way, revisions
have been made, such as age- and grade-level changes, additions, and
modifications in the achievement programs. But the ultimate purpose of
Missionettes?winning girls to Jesus Christ and teaching them to live
victoriously?has never changed."
source: Missionettes: About Us
"rainbow girls", "assemblies of god"
rainbows, "assemblies of god"
missionettes, "assemblies of god"
I hope this helps.