I actually asked a similar question to the people at the USRSA last year - though my question was more about people that were doing the Gallo-walking (so it would be a few minutes of running with walk breaks).
Their answer was that you need to run a mile continuously (no walk breaks).
But, that is just them, and as far as I (and this group) am concerned a streak is whatever you want it to be. This is all personal and everything, even on their site, is on the honor system.
As far as your particular question goes (because I do run intervals), I would honestly not recommend running intervals until your mileage is up to the point where you would be running at least a continuous mile warmup before doing the intervals anyway.
I hope this helps.
Glad to help.
You're off to a great start - keep it up.