Partially just because it's a fun word to say:
Their original model is consolidating micropayments to help make blogs and other new media more profitable; you send Kachingle X dollars per month, which they divide evenly between all the participating blogs you visit that month. Sounds like you can even fine tune the distribution of your donation by visiting your favorite blogs more often, so instead of splitting my $10 evenly four ways I could rig it to give one site $5 and $1.25 to each of the rest. Obviously no one's going to get rich on some fraction of my $10, but the idea is that a constant stream of nickles from a large mass of readers eventually adds up to useful amounts of money.
My mind went straight to non-profit fundraising when I read this. It's an electronic variation on the United Way model: we donate money to a central source that takes the massed quantity and divides among their member organizations. Biggest difference is that instead of being filtered through a political and frequently arbitrary selection committee, I can personally allocate my money. I'd be interested to learn the imact of this on tax donations; you can choose for the receiving organization to see your name, which to me means you can document your donation. Any tax attorneys/accountants out there want to comment?
Easy way to make this work without bending their model too much: post a blog for your organization. Doesn't need to be major, doesn't need to be great. Just be sure to update it regularly, encourage your members to participate in Kachingle, and remind them to click the "donate" button every time they come to the page.
Other thought: this becomes a good way to track use of different services, and demonstrate ROI to the members. Kind of a "pay to play" function, and a good way to catch those members that donate least but use the largest portion of your resources.
Let me know if anyone out there tries this; I'd love to hear how it goes.