Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your kitty ate something he should not have.
It may pass but since he ate the dental floss within the past 2-3 hours it's worth trying to get him to vomit it back up. String can act like a saw on the intestinal tract and if we can get it back before it creates any trouble that is best. Ideally he would see a veterinarian to have them give him an injection to make him vomit. Cats aren't as easy to induce vomiting with peroxide at home as dogs are, and since we are getting close to the time the floss may be leaving the stomach using something more likely to work is best.
If that absolutely isn't possible you can give him 1 tablespoon of 3% hydrogen peroxide orally per 10 pounds of body weight with a medicine dropper. Then gently place one hand on either side of his abdomen and move it back and forth to agitate the peroxide and get the peroxide bubbling so he vomits. This may not work, but it is worth trying.
If no vomiting in 10 minutes repeat the peroxide dose once.
If he vomits and seems to clear his stomach and be done I would check the vomit to see if the dental floss is present.
Once he vomits and clears his stomach, getting the floss out, to try and settle his stomach today you can try either:
1) Pepcid-ac (famotidine) at a dose of one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 24 hours.
These will reduce stomach acid and should help settle his stomach.
If you don't have any peroxide or don't think you can give it to him, get him to a veterinarian to induce vomiting.
If it he doesn't vomit, or vomits but the floss is not present then it may be too late to induce vomiting, the string may be out of his stomach.
After vomiting and giving an acid reducer to settle his stomach, or if you decide not to induce vomiting we can change his diet to try and help him pass this. Feed a homemade diet of 2/3 boiled white, skinless chicken, all fats and juices drained and 1/3 boiled white rice. Add 2 tablespoons of canned pumpkin, not pie filling, just pumpkin, to each meal for fiber if to help push the pieces through. Even if he vomits some of the floss it won't hurt to add pumpkin just in case there are small pieces left.
You can also give the petroleum based products used for hair balls, like Petramalt or Cat Lax, to help the floss glide through rather than catch. I would dose him twice daily until the floss passes.
If he doesn't vomit the floss there are symptoms to watch for that indicate he needs veterinary help. Trouble signs that point toward a need for an emergency veterinary visit are if he starts vomiting later, has a tense painful belly, refuses to eat, or runs a fever (more than 103F rectally) as those signs can signify a blockage and he should be seen by a veterinarian immediately. Surgery may be needed at that point.
Please let me know if you have any further questions.