I've been using LR3 for a few years now, and had to split my collection into multiple catalogs (I found that over 10k photos, LR would slow down so much as to be unusable). This is supposed to have improved with LR5, and indeed with the trial version I was able to merge all my catalogs into one (50k photos), and it's not too slow. Unfortunately, the Publish Services were not imported in the merge. I have close to a hundred Flickr sets linked to my collections, and I cannot find any workaround. Is there any unofficial documentation on peeking at the Lightroom database to copy those Publish Service settings? I don't mind if it involves a little coding/hacking, but have no clue as to where that info might be stored in the first place.
I've poked into this a bit in the past, and you won't like the answer much.
Publish services, because they interact with so many parts of Lightroom and with code blocks installed as plug-ins, are complicated beasts. Adobe's chosen to store their configuration information in the preferences file, not in a preset file.
The preferences file for Lightroom 5 (on a Mac) is in ~user/Preferences/com.adobe.Lightroom5.plist
Taking a look at the configuration block for my Flickr publish module (using Jeffrey Friedl's plug-in) it's about 2,000 lines of data out of almost 30,000 lines of preference material.
So if you're going to do this, it's going to be complicated and fussy. there are a lot of opaque content pieces that are likely specific to that copy of Lightroom and won't work if you simply copy/past them.
What I would do if I was going to go down this path: install the plug-in, configure it, and then try copy/pasting the folder structures from one preference to the other and hope it works. It might (it might not). Do this ON A COPY in case things break badly.
if you're trying to pull in presets from three different lightroom catalogs into one and make it all work by hacking presets, I expect you'll spend a lot of time trying and be unhappy on the other end.
At some point, it's faster and less risky to simply do it by hand and reinitialize things. That is honestly what I'd do. I've got a fair amount of experience geeking low level things like this and I wouldn't do it. I don't think this is a problem by Adobe, this is a big hairy beast.
One thing that can save you some (possibly a lot of) time: if you use a plug-in like Jeffrey Friedl's, it can look at your new Lightroom collection and compare it to what is published on Flickr and reconnect the two, so you don't have to republish everything.
Look in the "Syncing Flickr Data" portion of the plug-in's preference section in the Plug-in Manger (right-click the plug-in name in the left sidebar to bring up "edit preferences"). It'll solve some of the problems. Assuming that works properly (I've had problems with it, problems on the Flickr side -- it's API has been intermittently flakey for a while) that'll get you all of the images tied together and then it's a matter of recreating the collections and etc. Perhaps you might be able to do some of that by copying from one preferences file to another, but honestly, I wouldn't. Too many places for it to go wrong and no real way to debug or fix except blind luck.
This is probably a good place to start: Preference and other file locations | Lightroom 3.x.
I would have thought that publish services have their own folder and associated files similar to export presets that I am familiar with(\Adobe\Lightroom\Export Actions), but it appears as though at least some of the Publish Services data is actually located within the Preferences file. Take a look at this Adobe help file.
The above information might help you a bit, but I don't have first hand experience trying this out. What you may want to do is take a look at your preferences files and compare for differences, and possibly copy over records that appear to be similar to the Publish Services examples given on the page above. That might be a start to your solution.