If you absolutely have to have it - just put two solid black shapes that fit your screen over the content and have the first one fade out and the second one fade in over (the the default setting for fade in or out is .5 seconds - so maybe set these at .2 and .3 to have the transition flow across slides - change it as you want). Just make sure you set the slides to fill the screens at each break point in your design.
The html5 and responsive design settings don't allow slide transitions because they're built using AS3 (Flash) scripting in Captivate. Also, from a purely user point of view - you're adding to the size of the download and eating up more of my data by adding this transition - so ask your self if this trip is really necessary. I'm sure it's probably already been requested - but request a feature using the links to Adobe support - if enough people want this - I have a feeling it will get coded in a later update.