If energy flows into a chemical system and out of the surroundings, what is the sign of δesystem?

The internal energy of the system we can term it as total potential energy and kinetic energy. Energy flows out of the surrounding from the system then we can say that the internal energy of the final state is lower than its initials. The sign of ΔEsystem is negative.

ΔEsystem = Efinal - Einitial

=-ve

Efinal ∠Einitial.