That specific action would not impact your ranking in any search engine that I know of.

burn your feeds with feedburner and see results

Subscribing to your feed would not help ranking. If they syndicate your feed and include links back to your site it could help.

When a customer subscribes to our RSS news feed, does this have any SEO benefit please?

That specific action would not impact your ranking in any search engine that I know of.

Burn your feeds with FeedBurner and see results.

Subscribing to your feed would not help ranking. If they syndicate your feed and include links back to your site it could help.

I like when topics go like this! Emphasis above mine.

Talk to us about FeedBurner and your comments. I'm interested!

Here's my thinking. It's a Google service. Google utilizes the data from the various services you've signed up for. If I were a Search Engineer, I'd surely want to tap into all the data from those services and utilize that in determining the quality of the destination, yes? Kind of a no brainer from my perspective. And, the more Google services you've got going, the stronger the signals?

So, why wouldn't the search engines use Feeds as a signal of quality? And, how do they handle the indexing of those feeds? What's the protocol?

I've also got an expanded topic similar to this...

To Feed or Not to Feed
That is the burning question right now...
[webmasterworld.com...]

Sure, if you're running your feed through FeedBurner then Google has access to that data and could certainly weave it into their algo as a sign of quality. It certainly may be one of the elements of the algo, but it certainly doesn't seem to be a major one.

An increase in RSS feed subscribers will generally result from an increase in visitors to your sites...just as you may expect simultaneous increases in newsletter subscriptions, clicks on ads, etc. I agree that it could be seen as a sign of quality, but you'd have to be feeding the SE that data otherwise there's no way for them to tell how many people are subscribing.