Instead of using a retainer, I have been tying floss around my front teeth. Is this dangerous?

Retainers for ? An interesting idea ; these types of simple, creative ; inexpensive attempts to straighten or retain teeth have been tried many times but to no avail. Not only do they not work as well as conventional orthodontics, but yes.. They often do cause problems. You are better off doing nothing than trying this. See an orthodontist or general dentist for a consult.
Why ? Have you lost your retainer after orthodontic treatment? If so, then your best bet is to have a new one fabricated. Yes, there will be a fee, but you need to protected the investment made in your smile. Floss will not do the trick. If your teeth shift, it will cost more to correct the problem than just making a new retainer now.
Wear your retainers. Floss is not going to work as retainers..Let floss do the job of flossing and -wear your retainers to keep your ortho treatment stable..
DO BOTH! Retainers are meant to keep your teeth in the correct position. Flossing is meant to clean between your teeth. Two different things! must do both of them.

Related Questions

Is it still possible to floss the front teeth when a metal retainer is fitted to the back of the front teeth?

Yes. Use a 'floss threader' to floss between the teeth with the bonded metal retainer. Read more...
Yes. You might need a treader, which is a plastic type holder that looks like a soft needle to thread the floss between the teeth under the attachments. Read more...