I tried to find the essay you mentioned, but all I could find is this Gospel Reflections on Luke 12:49-53. If that is not the reference, feel free to roll my edit back and provide the right link, and then I have to revise this answer, which is based on Bishop Barron's Oct 26, 2023 Gospel Reflection.
I think you misread Bishop Barron. "spreading the fire" here means spreading the Holy Spirit love which comes down to the Church like tongues of fire on the first Pentecost. Because true love is based on Truth, those who don't believe Jesus (the Truth) will separate from us (because they cannot handle the Truth, though not in Tom Cruise vs. Jack Nicholson's sense), thus the division Jesus talked about in vv. 51-53.
Christ while on earth already has the fullness of the fire of the Holy Spirit (divine life) in Him (John 1:14). So Jesus could say in Luke 12:49a "I came to bring fire on the earth". But the Holy Spirit has not yet been given to the church, hence Luke 12:49b: "how I wish it were already set ablaze".
As priest, Jesus mediated the most holy love to humanity through His 3 year ministry of love. Bishop Barron wants to remind us that every baptized believer also has the inner fire of love by virtue of the Holy Spirit inside us. In addition (this is my opinion, not in Bishop Barron's reflection), we have the responsibility to welcome and let the Holy Spirit inflames our soul so our love can be stronger to approach the strength of Jesus's "fire", so in a sense we are also "keeper of fire" so it doesn't die (Bishop Barron didn't use the word "keeper"). But all believers are also called to be priest who needs to mediate our own inner fire to the world, hence "spreading the fire" of love.