How to ensure my audience can continue to open Flash slideshows?

One more thing, for building non-flash-based e-Learning courses and interactive content, look at Adobe Captivate.

https://www.adobe.com/products/captivate.html

For questions about Captivate, see the Captivate product community.

https://community.adobe.com/t5/captivate/bd-p/captivate?page=1&sort=latest_replies&filter=all

Now that Flash is dead, how can I ensure that all my users, mainly school students, can continue to get access to the content?

===========

Hi @baruch05,

Short answer:  You can't until you rebuild the site. 

Long answer:  Your site claims to be for "the 21st century" yet has both feet firmly planted in late 20th century web standards (fixed width, XHTML strict, etc...)  It's a shame.  These days sites need to be responsive to fit ALL web devices (mobile, tablet, laptop & desktop). Gone are the old plugins like QuickTime and Flash Player to support media.  All that is natively handled by browsers now. 

The site must be rebuilt with modern HTML5, CSS3 and JavaScript.  This should have been your web developer's #1 priority 3-1/2 years ago when the Flash Player End of Life was first announced. 

Announcement from July 2017:

https://blog.adobe.com/en/publish/2017/07/25/adobe-flash-update.html#gs.x59bnb

Your local college/university might have some web & computer science students who are willing to take this project on a low or no-fee basis.  Given your situation, it wouldn't hurt to investigate all avenues.

Best of luck!