How to get posts in community which have recently got kudos?

I'm not aware of anything that will give you exactly what you want. However, one option might be to use the Kudos message leaderboard, and restrict the date range:

http://lithosphere.lithium.com/t5/rest-api/bd-p/developers-rest-api?leaf-id=Community.kudos.messages.leaderboard#Community.kudos.messages.leaderboard

For example:

http://lithosphere.lithium.com/restapi/vc/kudos/messages/leaderboard?max_age=one_day

Unfortunately these won't be in order of when they received kudos. You could work this out with seperate API calls for each message.