Flint Michigan Police mace crowd waiting for BBQ.

You asked whether it's illegal to serve BBQ—presumably referring to food—after 2 a.m. in Flint, Michigan. Here's what I found:

Local Operating Hours for Food Trucks in Flint
According to Flint’s Zoning Code, within the UC (Urban Core) and DC (Downtown Core) districts, food carts and trucks are permitted to operate with extended hours—up to 3 a.m.
City of Flint
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That suggests that in downtown Flint (which includes Saginaw Street, where the incident occurred), it is legally allowed for food trucks or carts to serve food past 2 a.m., up until 3 a.m.

Conclusion
No, based on zoning regulations, it is not illegal for food trucks to serve BBQ at 2 a.m. in Flint’s downtown areas—service is permitted until 3 a.m.