Thanks to everyone that replied, the time/distance information is helpful!
It sounds like we should be able to make the walk without a problem (given the arrivals tip). Boarding passes will be in hand and we're both elite so should be able to clear security relatively quickly in T2. Also, carryon only, since it's an LAX-MCI MR.
Sorry about missing the SoCal Airport forum, I searched for LAX topics and it seemed like this was this place to post. I stand corrected.