Gliders can get fleas but I dont think thats the issue.
Did you know cats have a bacteria in their claws that can kill a glider- even with an accidental scratch. I've heard of too many gliders that get killed by cats and dogs.
Please read this discussion
http://www.sugarglider.com/glidergossip/topic.asp?TOPIC_ID=16252
I understand you think your pets get along, but what if the cat or the new puppy accidentally hurt them? I'd never be able to forgive myself if something happened that could be prevented so easily.
I urge you to get your glider another glider buddy to be friends with.
But about the flea thing. I don't know, i've never heard of a glider getting fleas my best advice would be to call up your vet and see what they have to say.