It sounds like you're actually referring to the TNG/VOY combadges, if you're referring to the chirping "insignia" on the chest (usually called the TNG or VOY Combadge.) If that's what you're looking for, here's what I know. I'll warn you, this ended up being a bit of a doozy, so the TLDR; Read the first paragraph, get the $65 Amazon badge if you want an easy and decent looking solution. If you care about accuracy, or just want to hear me ramble about commercially available combadges for awhile... read on:
There is a commercially available TNG combadge currently available on Amazon for around $65. It's a decent little thing with a soundboard for chirping and is even Bluetooth compatible, although I've heard it's Bluetooth functionality leaves a bit to be desired. In terms of accuracy, the geometry of it is all wrong, it's way too thick and way too tall compared to a screen used one. The paint job is also supposed to be a little bit reflective, but they've gone for what appears to be a completely matte look. Preferable, compared to the completely shiny look that badges like the QMX badge have. It has a decent enough paint job for what is essentially a toy you can buy off Amazon. And I mean, they did fit an entire communications device inside of a tiny combadge, so what can you do! Honestly, if you can swing that much for one, I'd go for it. It's a fun toy, as would any chirping combadge be, and it sounds like you're not gonna go super crazy if it's not perfectly screen accurate.
Link via Amazon: https://www.amazon.com/Star-Generation-Bluetooth-Communicator-Badge/dp/B0777S47VQ/
For a cheaper, less accurate option that has some possibility for making more accurate: in the Mid-90s Paramount released a line of "Talking Communicators" that chirp and play a voice line. I haven't gotten the TNG or VOY ones yet, but they don't look supremely accurate dimensionally compared to the real deal. Would be great for a basic cosplay, though! The main benefit is that they're magnetic and use a strip of magnetic surface, so theoretically, you could use your own custom accurate badge with a magnet on the back, and use the same electric piece to get the sounds and everything. Only problem is that the electric backer is a bit bulky imo, and might show through on a costume if the costume is super skin-tight and doesn't have a lot of slack around the chest. Also, it barks voice lines at you, too. Just search for "star trek talking communicator" on eBay for them. They made one for Klingon, Bajoran, TNG, and VOY badges.
Interesting note: The Klingon Badge is, for some reason, 1 to 1 with a real badge! It's perfect! I don't know why that one is so accurate and the TNG and VOY ones aren't lol. I'm still waiting to get the other 3 and compare them to my production made castings. For size reference to the speaker, here's a comparison between my Rodd.com TNG combadge and the Klingon badge + the speaker, just so you know the kind of tumor you'd have under your shirt:
Now, you didn't ask for this, but if you're going for ACCURACY with NO NOISES, be warned, this can be a bit of a rabbithole!
If you are actually chasing an extremely accurate one, find an independent artist around here who can do you up a casting from a screen used badge, with the right paints and all. Community members tend to do great jobs on badges, albiet people have kinda gone into hiding because of Big P+ sending C&Ds to people. I'm not sure who around here does combadges, but a few searches for "combadge" "commbadge" "communicator badge tng" will probably net you some results. Might even want to put our a WTB offer for one, and I'm sure someone is still making them in private. You can also look on Etsy, lots of options pop up on there and you'll be able to tell pretty quickly which ones are accurate and which ones aren't by the people who actually care to paint them correctly. As a last resort, seek out secondhand Roddenberry.com or Scott Nakada (XScapes Props) badges. They pop up from time to time and are the best of the best, but go for $50-$100 depending on how nice of a seller they are. Scott's are a little duller in shine compared to the Roddenberry.com badges. While the Rodd badges are apparently supposed to be the most accurate, I prefer the duller look as it looks better on camera/in person. IMO.
If you're DIY inclined, and own an SLA printer, I made a 3D printable badge that's based off my production-era casting, as well as a lot of hours of research to create a best mid-level badge that's accurate up to about 0.5mm. Paint instructions are included in the description.
If you want something off-the-shelf that's pretty accurate in terms of looks, Fansets just put their TNG combadge back in stock. I've never seen one of these up close, just ordered one myself, but their VOY badges were well received due to the way more accurate color scheme compared to the QMX badges that were the only available option beforehand. I'm not as convinced however, they could do a better job on the choice of paint. It's supposed to be more "sparkly" and metallic as it's automotive paint, but Fansets seemed to go for this brushed gold look. Not a big fan, but I'll have to see it for myself to be sure. This is however the "most accurate" option currently commercially available. If these go out of stock before you see this, they also have the pin version which might be in stock.
BACK IN STOCK We proudly present the Delta from Star Trek: The Next Generation!! It's the one you have been waiting for! This delta comes to you directly from Star Trek The Next Generation. It is full size. While manufactured with FanSets normal attention to detail this was not created to be...
OUT OF STOCK We proudly present the Delta from Star Trek: The Next Generation!! It's the one you have been waiting for! This delta comes to you directly from Star Trek The Next Generation. It is full size. While manufactured with FanSets normal attention to detail this was not created to be a...
You probably didn't mean to ask for all this info. Whoops! But I figured I'd give you everything I know and hope some of it is helpful. If anyone else sees this and I'm wrong about something, please be nice, I wrote this last night at like 2am.