Hi Samantha,
iPads and iPhones do not support flash at all, even if you do a jailbreak it will still not allow you to view flash content.
To be honest it depends on what the online school actually offer within the flash, as you said there login is based around flash I presume it will involve a whole re-design and re-code to replicate it within HTML5.
Something you should note, HTML5 does not allow as much interactivity with the user, it will probably have a look and feel as an online website, meaning text will be static as well as images. Videos can be incorporated but again this is with minimal styling.
Anyways, to answer your question, if the whole program is based around flash it will probably require a lot of work to get it to have a similar look and feel to the flash. Ask the school if they have considered it, you never know, they might have one available as iPads are currently the new trend and most companies are trying to roll back to support Apple devices.
Hope this helps.