In a large bowl stir together cream cheese, sriracha, and ranch until fully combined with no clumps of cream cheese remaining. Stir in chicken (it'll shred into smaller pieces, that's fine), then fold in shredded cheese.

Lay out one flour tortilla. Spread one sixth of the filling over the tortillas surface, leaving about 1/2 in of the far edge uncovered (to allow for filling squishing while rolling). Beginning with the side nearest you, fold over the edge then continue to roll tightly to make a "log". Repeat with remaining tortillas and filling.

Wrap roll ups tightly in plastic wrap. Refrigerate at least 2hrs, or up to overnight, to firm up. Cut into half inch slices, arrange on a platter, serve, and enjoy. Drizzle with additional sriracha for extra heat.