1. When mentioning a word you've heard in the hope that people think you have some clue what you're talking about you need to stay up to date. Rainbow Tables were 2008, this is 2018, try "Blockchain" instead.
2. No. Rainbow Tables are an improved time-space tradeoff. For situations where a time-space tradeoff is almost good enough, Rainbow Tables can take you over the line. Where you aren't even close (as is the case for Signal), it doesn't matter.
For the obsolete LM Hash a straight time-space attack needs maybe 50TB of disk to break it with 100% accuracy, which back in 2003 would have been really expensive. Rainbow Tables often shrank this to about 30GB, with < 1% penalty to recall and a modest additional time penalty, so it was made much cheaper.
With a Signal ratchet you need a lot more space. Imagine all the disk space that exists in the world today. OK, now imagine that this space doubles every year somehow, and that keeps happening for the next 100 years, and you have all that disk space for your project of breaking a Signal connection. You are still nowhere close, even with some very generously estimated Rainbow Tables.