Flash Slideshow apps are basically a generic player created in Flash, where you supply your images, & use the code snippets provided with the software to insert it on your web page. Adobe owns Flash [just like Acrobat [PDF]], releasing older, more limited versions of the tech for free. I think it's safe to say that many Flash slideshow apps use 3rd party tools to write their players. As with non-Adobe PDF software, you might encounter more glitches, but the primary problem is Flash itself -- you're eliminating a good portion of your potential visitors just by using it. Many PC/laptop users don't have Flash installed, plus there's all those tablets [195 mill sold in 2013] & cells [the number of *active* cell phones is expected to reach 7.3 bill in 2014].
2 minutes using Google came up with...
Visual SlideShow
http://visualslideshow.com/
Easy to Use
Just drag&drop your photos to Visual SlideShow Maker, customize look and feel and publish your web slideshow!
Flickr and Photobucket support
Embedding albums, images, and slideshows
https://support.google.com/picasa/answer/66969?hl=en
Flickr Slideshow
http://www.flickrslideshow.com/
BarelyFitz JavaScript slideshow
http://www.barelyfitz.com/projects/slideshow/
This is free, open-source software...
Use the Slideshow Wizard to create your slideshow - just copy the pictures onto your own website, and paste our HTML into your web page.
Free Slideshow Creator - We Make Slideshows for Your Website
http://www.cincopa.com/media-platform/services/create-slideshow
How to create an image slide show on a webpage
http://msdn.microsoft.com/en-us/library/hh920769%28v=vs.85%29.aspx
WordPress Slideshows
http://en.support.wordpress.com/slideshows/
http://www.wikihow.com/Embed-a-Picasa-Slideshow-in-Your-Blogger-Blog