If you give sugar gliders a lilac branch, that definatly was not sprayed with any chemicals, that still has the flowers on them, is that safe? I mean, if they happen to bite the flowers, will that be toxic to them?

According to this site, Lilac's are a safe plant to give to suggies. But, you must be 100% certain no one around you is spraying, your city isnt spraying, etc.

http://www.moondance-sugargliders.com/sugar_glider_plant-tree_information.htm

Edited to correct link

Well, my city sprays for mosquitos every year, but they didnt pray this year yet, would it still be alright to give to them, or do the chemicals stay inside it through the winter?

I would be afraid the chemicals would get into the soil the Lilac bush is growing in. I wouldnt give it to them - to risky. And thats a shame because they would have a grand time with the branches.

Our city also sprays for mosquitoes. It doesnt help to complain, either.

Well, I looked up the thing they spray and its called Anvil 10+10, and everywhere I looked it said that it goes away after a few days, and has a half life of 18 days...so I think that means that it would be unaffected come a year.