Do you want Google Image search to send the traffic to Flickr? Can you get good traffic data from Flickr? Also, have you checked to make sure that Flickr doesn't block Google?
I would advise hosting it yourself. The potential advantage of getting links, sharing of your images, search traffic etc outweigh the effort involved in setting up a gallery IMO.
If possible, set it up so that each image you add creates an actual page -- the page displays the image and the caption and maybe the option to download it at higher resolution. That's a lot of fresh pages of content meaning a lot of opportunity to rank for long-tail keywords. This traffic may not be highly relevant to your business, but you may get some links and social sharing activity out of it, depending on the nature of the images.
When targeting google image search, keep in mind that image traffic tends not to interact with your site and does not usually meet conversion goals. This is especially true with recent UI changes in image search. Google is showing such a large number of results in a gallery, even if you are very well ranked, you get a low click through rate. When folks do click through to you, Google inserts an overlay with the full sized image over your site. Many (most?) users don't close the overlay to get to the page. Even those that do get to the page, seldom visit other pages.
deadsea, I agree about image search, it's close to useless. I'm not talking about targeting image search, I'm talking about targeting regular search with image pages. Some people scroll past the image search and click on the regular listings, even for keywords that are clearly image searches. What they're looking for is a gallery of images related to their keyword, not just a bunch of single images lifted from random sites.
This traffic can be much more useful than image search traffic.
I host all my own niche trade related images using both regular hand-built pages and a Coppermine gallery.
Once you've wrapped your head around all the Coppermine options available it is an awesome piece of freebie software.
It's very easy to set-up a basic gallery yet has some very powerful features once you get used to it.
If your hosting uses CPanel then it's most likely already there ready for you.
IMO it's always best to host on your own domain.
IMO it's always best to use images in context, within articles or at least on the same pages.
IMO not many gallery scripts do well from an SEO perspective.
Thanks to everyone for their feedback. It does seem that a custom image gallery makes more sense from an SEO perspective, and in terms of spent resources.
On a similar note, if the target of discussion was now switched to video and one had to ask about a custom video gallery VS YouTube, what would your thoughts be then?
>>custom video gallery VS YouTube
you want your competitors ads to show on your videos?
Surely compared to the branding and exposure it opens up for our business, competitor's ads are only a small evil?
With no YouTube channel we get zero impressions. With a good YouTube channel we get many impressions with a small percentage going to our competitors?
The latter still seems like a more desirable outcome..
I've not previously thought about trying to rank on image search and this thread got me doing some research on one of my sites that has a photo gallery.
My site uses a CMS that gives uploaded images a name like 126.jpg this is clearly (looking at my images SERPS) not a good thing. You need a gallery system that allows you to keyword your image name, alt text and caption.
I personally like jquery Galleria which I use but have no idea if it is any good from an SEO point of view.