Upvote:4
I found two schools of thought on this.
School 1:
There is not and never has been any official organization overseeing all Pentecostals, and there is not really one single founding church of the movement.
Pentecostalism is a set of beliefs that evolved over time among a lot of independent churches, so there really is no single founder. The earliest Pentecostal churches evolved from what they were into that philosophy, as it evolved itself around the beginning of the 20th Century.
No one person or group founded Pentecostalism. Instead, isolated Christian groups were experiencing charismatic phenomena such as divine healing and speaking in tongues. The holiness movement provided a theological explanation for what was happening to these Christians, and they adapted Wesleyan soteriology to accommodate their new understanding
It looks like some important early churches in the founding of the movement were the Christian Catholic Apostolic Church and the Christian and Missionary Alliance churches. However, neither themselves became Pentecostal.
School 2:
The movement was founded by the Azusa Street Revival, which ran from 1906 to 1915 in Los Angeles. Early on they were drawing huge crowds. For the first couple of years they even put out a newsletter with an international circulation, the title article of the first issue of which was "Pentecost Has Come"
With all the attention, lots of people from like-minded congregations visited (or just read the newsletters) and took back what they learned there to their own churches.