if teamspeak is affecting your other programs network performance it's eating too much bandwidth. if teamspeak doesn't offer traffic modulation I suggest you move to mumble.
flushing your dns can be accomplished as follows:
go to start > run > type in: cmd /k ipconfig /flushdns > hit ok
flushing dns basically resets the preresolved server path your packets take on the route to their target, it's possible that one of the servers in this path is being a turd and when you flush dns it will take a little longer for your first time connection but once the dns is cached again it should improve. This was a relatively common problem about 4-5 years ago, ISPs have gotten better since then but you never know.
renewing your ip could be done the same way (/renew parameter on ipconfig function) on local intranet, but to get a new IP from your ISP you'll need to power down your modem for 5-10 mins or so then plug it back in.
I was looking for bandwidth controls, and could find nothing, however merely having it on caused the problem, not attached to a server, forced to directsound vs auto and problems went away. it was causing a stuttering and rubber banding. Just a thought.
hmm, very strange side effect, but afaik team speak is similar to ventrillo and I abandoned that prog cause it was rather garbage. Been using mumble for almost a year now, very good experience and very little problems.