What fitting do I need to carbonate a glass flip top bottle

What you ask for does kind of exist actually. You can use a counter pressure bottle filler to inject only CO2 into a bottle. It's sealed by a cork. I do not know the max PSI on the cork. But you should note, I have seen several videos where people use soda stream bottle carbonators with flat beer and they do not get a good result. Not enough CO2 dissolves.

Counter Pressure Bottle Filler with Cork

You normally would carbonate in a keg and then use a counter pressure bottle filler to fill your bottles with well carbonated beer.

Easiest way is to do bottle-conditioning. It only takes about 5 days. You could use pre-measured sugar drops for this to get done fast.

Side Note: Champagne bottles are designed to take a lot of pressure. I think 70-90 PSI. There are small ones available.

I would highly recommend against pressurizing directly into glass bottles. There's no feedback mechanism as there is with the flexibility of plastic bottles.

As others have commented, beer bottles are rated somewhere around 3 volumes of CO2. (That's roughly 45 psi - volumes * 15psi ). Remember that's on average for the manufacturing process. Some bottles will be weaker than that, and it's not a risk I'd be willing to take.

Champagne bottles are rated for typically 8 volumes, or 90 psi. They are available in 375ml bottles from at least one wine-making shop on the west coast.

Your best bet is to carb in a keg and then bottle from the keg. The added benefit there is an even greater reduction in yeast transfer to the bottles.

I've only seen the ones for plastic bottles. You usually squeeze the bottle a bit, then fill it, then screw on the co2 valve (while still squeezing). You can stop squeezing once the valve is in place. Then you pump co2 in. Naturally, the bottle expands, and that gives you a good idea whether you should put in more or not. Clearly, this does not work for glass bottles, and you may get no warning on how much is in them and how much they can still take.

See also the accepted answer of Do some beers really require special bottles due to pressure?