A conflict of interest only happens in this situation if the person in question allows corruption on the roles.
I used to think you could not be. However I changed that to should not be, because I have known someone balance it very well with great integrity.
Can it be done? Yes Should it be done? Probably not.
Take a look here for more http://adaptagility.co.uk/can-the-scrum-master-also-be-a-developer