All that being said, I don’t think the conference can kick Baylor out - as much as they deserve it.
Possible, maybe (depends on interpretations of vague bylaw statements). Probable, no.
Following the yellow brick road on this one...
Baylor has already been sanctioned once by the conference, so anything additional could result in a withdrawal vote ("withdrawal" is the technical term for being kicked out). It would probably fall under "failing to take action / taking actions contrary to the interests of the conference", and would require 7 votes out of 9.
If such a vote happened, it could be up to two years before they're actually gone. The timeline would depend on whatever date the event in question occurred. Theoretically, it could be retroactively applied to something that happened in 2016 or 2017 -- in which case they could be gone as early as June 30, 2019. Otherwise, it would likely be June 30, 2020.
Additionally, because a vote to kick a school out is viewed as a "withdrawal", that school might also not get its share of the revenue distribution for that interim period between the vote and the effective date.