I've lived the cliche...you can lead a horse to water, but you can't make it drink. So, how about doing this the other way around?
Instead of "[pushing] training and other relevant material to their screen" how about incenting them to want to learn, to seek it out?
Learning *is* a lifelong endeavor, and those who understand this are the people I want on my team. They are the ones who will take the bull by the horns: find it, figure it out, read, ask, etc. This is not a genetic trait...it is learned behavior.
FWIW, I think if you find an application that pushes stuff to their screens, you will end up with 80-100% of unread material. Or the material will be read, but it will not be absorbed/understood. But if you find a way to incent them to want to gain knowledge...then you'll be moving mountains.