I love Flea's tone on MM too. A month or two ago I listened to it again and was just blown away by 'Magic Johnson.' Based on some of the videos I've seen and interviews that I've read, I'll try to share what I know.
I believe early on he was using Spectors, as he's in some of the early videos with one. By MM he was using the StingRay, at least live, through GK heads and big Mesa cabs. He was also playing GHS Boomers. I believe in an interview he said that he used whatever was in the studio at the time of the recording. Some of the MM parts sound to me like they were done on a P-Bass (the father of the StingRay.) Also check out Young MC's 'Bust a Move' for some pure Flea. Yeah, it's cheesey, but the bass is awesome.
For comparison, 'Under the Bridge' and 'Give It Away' were recorded with an SR5, going by the video 'The Making of Blood Sugar Sex Magic.' Also, Rick Rubin is there basically telling him how to play a minimal bassline. I believe that he did most of One Hot Minute with an Alembic Epic, not positive.
I got a chance to see the band live a few years ago, and the whole sound was awful -- all midrange. He was also WAY overplaying on some of the awesome lines from BSSM, such as 'Give It Away.' Every other band that day had a great sound, except for them. And the singing was pretty off-key.
Overall, I think *most* of the credit for the bass tone on these albums needs to go to the engineer and/or producer. Although I do love his playing overall and that's the important thing. Just my opinion...