Fitbit and Running re calories burnt??

You shouldn't add the run as a specific exercise as the fitbit is recording it via step-counting. It will give you an appropriate calorie burn due to the speed of the run.

I use a run watch, which will record the run, and fitbit blocks out the time spent running/steps and recalculates based on this to prevent double accounting.

Basically, if you are doing any exercise where it imitates steps, let the fitbit do it and don't log in MFP. If you are swimming say, or cycling, then log it but be sure to include the time. If you are keen to see that you did an exercise, you can manually change the calories to '1' for example.

You will notice that you now have to enter the exact time you started your run in addition to duration. This is because MFP will adjust for Fitbit steps during that exact time.

So for example, let's say you started running at 6:43 a.m. and ran for 28 min. You will enter this on MFP and let's just say that MFP comes up with +250 calories burned.

During that same 28 min., let's say Fitbit adjusts +280 calories.

Now, let's say for the rest of the day, Fitbit would adjust +120 calories.

IF you don't log your run on MFP manually, you will get +400 calories from Fitbit.

IF you do log your run on MFP manually, you will get +370 calories (+250 for the logged run +120 outside of that from Fitbit). That's my understanding, though there maybe someone that has a different answer.

So the short answer is: No, you did not double-log.
However, it is best not to log step-based activities manually because Fitbit is expected to be more accurate than manual logging.

I allow my Garmin to load my actual workout but then I delete the supinate steps entry. That way I don't double count and since calorie burn is notoriously over-optimisic this helps account for the delta.