Last month, Adobe announced they would not support any further versions of Flash for Android devices. As a result, on August 15, Flash will disappear from the Google Play Store forever. With the end of Flash for Android, Flash is officially on its deathbed.
However, from an SEO standpoint, Flash still has its place, in video and audio files. Until changes are made to how search engines index HTML 5, the best SEO practice is to offer content in Flash, HTML 5, and basic HTML.

The Last Few Years

A few years ago, Adobe declared that Flash was supported on 99% of all internet browsers, both mobile and non-mobile. That stat was likely exaggerated, as their study had a limited sample size and did not include many Linux-based browsers. However, the point still stood that it was an extremely common programming platform on the Web.
However, when Adobe announced the 99% stat, there were only 10 million active iOS devices in the world. Now there are 410 million, and counting. Apple still refuses to offer Flash support on any of their devices. This is a huge number of devices from which Flash is cut off.
With Adobe canceling Flash support for Android, and smartphones selling at an unprecedented rate, it is likely that worldwide Flash access will be exceeded by HTML 5 access within the year.

The Next Six Months

It is challenging to find exact numbers for the reach of Flash or HTML 5, but it is possible to make some rough estimates. The total number combined number of active Android and iOS devices is in the range of 900 million, and will exceed a billion by the end of the year. There are about 3 to 3.5 billion devices running internet browsers. Most studies have found that about 75% of browsers run HTML 5. So, the likely present and future reach of Flash and HTML 5 is as follows:

Making the Switch

By the end of the year, HTML 5 will be accessible to more internet users than Flash. This trend will likely continue into the foreseeable future.
New websites should minimize their Flash usage and maximize their HTML 5 usage. However, for purposes of SEO, it is still too early to phase out Flash content entirely.

Why Keep Flash around?

Firstly, websites should keep Flash content that they have already produced. Flash is still used by billions of browsers, and will likely experience a slow fade rather than a rapid one. There are still a lot of Flash-dominated areas on the Web, such as online games and smaller video sites, that will continue to drive Flash support for browsers well into the future.
Flash and HTML 5 each have their own pros and cons when it comes to indexing web pages. In general, HTML 5 pages take less effort to index than Flash. However, search engines have yet to support HTML 5 video and audio. For the best SEO, web designers usually have to offer HTML 5 and Flash resources. Here are the advantages and disadvantages of each.

• Flash and SEO
  Search engine bots have been notoriously unreliable for indexing Flash pages. Flash cannot be used for navigation without hurting SEO. If Flash buttons are at all used to navigate a site, spiders will likely flag that site as having problems with transparency and navigability.
  Video and sound files are too difficult for search engine bots to understand, as are many types of Flash objects. In most cases, the only things that search engine bots notice are the filenames of Flash media files.
  To help the little bots along, web developers have typically used extremely long and keyword-heavy file names. They have also made fully HTML versions of their web pages with the exact same duplicated content as their Flash pages. Proper SEO practice holds that every Flash landing page should have a near-identical HTML landing page to go with it.
  This just creates a lot of extra hassle. Whenever a website is altered or updated, developers have to change both the HTML and Flash resources to ensure proper indexing.
  Some of these problems were solved in HTML 5. However, some of them were exacerbated.
  
• HTML 5 and SEO
  With HTML 5, there is no need to separate out navigational tools and write them in basic HTML. Search engine spiders are capable of reading HTML 5 and indexing it correctly. While it is still good practice to write alternate landing pages in basic HTML, it is not strictly necessary.
  However, HTML 5 is even worse than Flash for indexing video and sound files. HTML 5 video and audio files work as separate HTML 5 play pages that are embedded in HTML iframe objects. At the moment, it is extremely difficult for search engine spiders to identify how video and audio pages fit into larger web pages, and they often overlook the markup in play pages. Major search engines like Google have yet to announce any changes to this in the near future. The only way to overcome this is to provide video and audio files in both HTML 5 and Flash.

Unfortunately, at the moment, the shift from Flash to HTML 5 means more work for SEO experts. HTML 5 is undoubtedly the new standard, but is not supported by search engines enough to totally replace Flash. However, this may change soon, as HTML replaces Flash as the standard for dynamic web media.