I just did this for a two-book series. These books had only been with Amazon, and I wanted to update covers, change titles, and distribute wide.
I'm an idiot and didn't plan very well. I submitted the changes to KDP on 3/19, they went live (according to them) the next day, but no changes were visible. Took 2 days for the new covers to show, but the sample and Look Inside were still old. Today, 3/26, one of the books updated. The other still hasn't. I made the mistake of announcing my new covers and titles on the 19th, and readers were eager to download, but they balked at seeing the old stuff still on the website (and I don't blame them). Supposedly, buyers who already have the book should be able to sync their Kindle libraries and get the new version, but it hasn't worked for me yet, and I'm waiting to hear back from Amazon about this. Ugh. I should have waited to announce the changes until everything had gone through.
At the bottom of my blurbs, and on the copyright pages, I put that the books were previously published as (FORMER TITLE). Not all authors do this, I've noticed, so I don't know if it's relevant or helpful. These books were pretty much dead, so even though the conversion process has been irritating for me, it hasn't impacted my sales much.
I also have paperbacks of these via Createspace, and I stopped their distribution before I started this process. You can't just update Createspace titles - you have to delist them, then create entire new books. It's been about two weeks, and the old books are still for sale on all the distribution sites (like B&N). That process, of delisting wide, is very slow. Again, poor planning on my part.
I'm already seeing sales on other sites (iBooks, B&N), but I don't know if it's because a) I suddenly went wide, b) my new awesome branding, or c) I put the first book free. This publishing thing needs to come with a manual. If I had to do it over again, I'd make one change at a time, planned well in advance, so I could properly track how each change affected the bottom line. Sigh.