Is there a universal phonotactics database available online?
"Universal" in the context of language means "all languages". There isn't even a universal phoneme-inventory database. A phoneme inventory is the product of a lot of analysis of a language, whereby you can conclude that in Mongolian (a major national language), there are phonemes /u/ and /ʊ/ – this wasn't understood until the 90's. It requires many orders of magnitude more analysis to arrive at the distributional regularities that constitute a statement of "phonotactics". To this day, it is not definitely decided whether nonexistent sequences in English like "snin", "slill", "spep" are merely accidentally missing, or are they systematically excluded.
There was a plan to have a large but not universal database, which did not materialize.