There was a max streak badget, e.g 95 days.
It was removed with Ziggy website update, but is still available on the Android app (maybe you need an older version - at least it works for my version).
You are right. Once you have completed the courses, the website will not show anymore the streak data.
AFAIK the mobile app still does it.
Even the website does NOT show you the streak for completed courses, it is still incremented.
You will receive Pro announcement marketing popups from time to time, once you hit the 5 / 10, etc. streaks, where they want you to offer 20% or 50% Pro discount.
Summary:
- there is no DuoLingo global streak
- reviews are not counted on the web portal for completed courses
- max streak badget has been removed on the web portal, but is visable on the mobile app
Tip for reaching 365++ streaks:
If you start a bigger 3000-5000 course or / EasyAcademy >7500 words Polyglot course (multiple L1 languages shown), you need to leave out 5-10 words, or half-plant them to learning-steps 3-4 and not complete the learning until step 6:
Then you could continue to review the big big Memrise language course for reaching a 365++ day streak and have the streak also shown on the website per course…and you can work on improving your last max streak badget (which you can check on the mobile app).
This concept will not work that good for the offical 1-7 + Basic courses, as they are too small and you can not easily leave out 5-10 words or a “not so important course” level", like language names for pronunciation, alphabet, etc.
SR Overdueness (missing):
The other big problem is, that Memrise has no code for overdueness: This means, if you do not review your completed courses daily / weekly, it will not increment the next SR interval higher than the next standard Memrise level.
The best would be to let the completed Memrise courses finished but export them to Anki, where you will have additional statistics, and continue the reviews there.
There is a plugin called Memrise2Anki (I can not test it right now).
My personal experience is, that with user scripts installed like “all typing” (by Cooljingle), I hardly review my completed courses (I 1-2 times did for 1-2 and a few times for Basic, but lately 1-5 is somehow “untouched”, so 3-5 was not reviewed that many times!)
Why?
Because too many “words” (incl. phrases/sentences) in the backlog queue.
Typing full phrases / sentences daily is too much work., but really tests RECALLING in the L2 target language.
So a self-rating answer concept like Anki might not be bad to get you back on track with completed courses, especially the 1-7 + Basic ones.
Multiple-choice - as implemented right now by staff - is not that good as the answers 1-8 are not hidden; you can guess, you get hints, etc.
There better should be a new review type available.
Example:
Camilo’s DuoLingo user script “DuoLingo tree enhancer” has the option to hide texts and pictures for e.g reverse tree courses.
If you scroll over with mouse pointer, the text is again readable.
Something like this might be good to have on Memrise as an “typing alternative”.
So yeah, my “concept” for 1-7 courses are to switch to Anki (and import my current SR intervals).
This will be the next benefit: There is no max 180 days SR interval on Anki, like there is in Memrise.
Any questions? 
