Flash is definitely what you need to be able to animate properly.
The other way would be to export a series of gifs and do an animated gif but it’s a slow and laborious process.
I’m not very good at Flash either but I’m pretty sure you can export Illustrator layers (rather than artboards) to Flash.
Once you’ve got the stuff into Flash you can fine tune the timing.
Maybe someone who is more competent at Flash than I am might like to chime in.
