I recently got a new ring and it is alittle on the heavy side. I didn't think it would be a problem when I played the flute but it just feels to be playing with the extra weight. Will this possibly slow me down? Also, will my ring possibly scratch my flute

if it has some kind of stone in it it might get scratched but as for playing with it, plenty of people play with rings on if it is not to heavy for your finger you should be fine with it, if not take it off and place it in your case whilst you play then put it back on when you are done,
If it is in your case you are unlikely to forget to put it back on.

Here's a novel idea, take OFF the ring when you play. Wow.. I am smart!!!