The pair worked together in their Atoms for Peace supergroup, along with drummer Joey Waronker, Mauro Refosco and producer Nigel Godrich last year.
"It influenced me being around Thom," Flea explained. "He's an unbelievably great musician and a beautiful man. He's so pure as an artist. It's less that I would try to copy him and more that just being around someone who channels really powerful energy is beneficial.
"It's a relationship I will always hope to nurture."
Flea added that he has also enjoyed collaborating with the likes of Damon Albarn and Patti Smith during Red Hot Chili Peppers' two-year hiatus, but that he is now glad to return to the band.
"[T]he Chili Peppers are a different entity. It was inspirational to play with Thom, Damon and Patti but being in a band with Chad [Smith], Anthony [Kiedis] and Josh [Klinghoffer] is my home. It's a beautiful thing."
Speaking about working with Albarn's Africa Express project, Klinghoffer added: "It was like a musical field trip. We had outings every day. It was like summer camp - and then Flea got lost and when he was lost, he went through a lot of emotions which is reflected on the album. It's the point where we were starting to really come together."
Red Hot Chili Peppers will release their tenth studio album I'm With You on August 29 in the UK and August 30 in the US.
> Red Hot Chili Peppers live gig to show in cinemas
Listen to 'The Adventures of Rain Dance Maggie' by Red Hot Chili Peppers below: