file_get_contents will do the trick for reading data most of the time. Unless you get it in a http post or get request of course. Then it's $GET or $POST.
json_decode will parse the input string into php arrays/objects.
But, the data needs to be parsed and interpreted. And unless there exist a standardized spefiication of how to express sqlite queries in JSON, you are the one who will need to parse your data and decide what to do with each item. If there is a standardized specification, then there are likely tools/libraries to do this part of the job for you.
Without such a standard, for, foreach and possibly recursion will let you go through the unserialized data. And there are a heap of array functions that may be helpful as well.
You are the one who (hopefully) knows the structure of the data, and what any specific thing would mean. Perhaps there's an array element or object member called table, which in turn is an array with table data for tables to be created. Or it might exist in just that way but should be considered data for insertion into that table...