I have tried making ink from red roses a few times but haven't been satisfied with the results. Admittedly, all those attempts had problems that I was aware of right from the start. For example, one (forsaken rose) was made using dried red roses, boiled for a long time in water and little vinegar, and fixed with gum arabic later. This turned out to be pretty brown, which is not surprising. This time around I did cold extraction and learned more about the chemical properties of the core pigment involved, anthocyanin.
Here is how the end result looks like:

Since I didn't check the exact pH and also didn't filter this out well, I am not putting this in any of my fountain pens yet. But the liquid works well with dip pens and brushes.

The process I followed was simple. I started with a bunch of washed red rose petals, added hot (near boiling) water over them till they were covered, mashed a little and let them untouched overnight for extraction. Next day, I removed the petals and let the solution concentrate by natural evaporation for around a week. You could reduce this time by using a flatter container. In fact you should reduce this since more time in the open starts fermentation and other decomposition processes which is something you don't want1.
Other than a good end result, another moment of joy was seeing the ink behave at different pH levels. This is a well known behaviour of anthocyanins and I was able to get colors from deep red to green-yellow just by using acids and bases present in my home. So I ended up making a few variants:

For fun, you can also make a rough pH scale using any anthocyanin based color. Here is how this ink behaves when mixed with some household items:

Lime juice moved it closer to the original color of the petal which was more cherry red than rosy, but it's too acidic for pens.
Once I am done with my current batch, I will try making this ink more stable and safe for fountain pens.
Footnotes:
Not sure if they are necessarily bad since I stopped just when fermentation seemed to start