Conformational dynamics of a single chain of wormlike polyelectrolyte xanthan polymer has been investigated in the external flow fields by employing a well-suited coarse-grained Brownian dynamics simulation. This goes beyond other simulations, which do not consider the hydrodynamic interaction between pairs of beads in poly-electrolyte polysaccharide and the long-range electrostatic screening effect. Conformational properties, such as the radius of gyration and the static structure factor, were unchanged with the flow strength parameter (i.e., Weissenberg number) in the uniform flow. However, influences by flow strength as well as flow type were evident in both simple shear and extensional-like flows with non-zero velocity gradients in flow regimes, commonly exhibiting a sigmoidal transition in the radius of gyration. Transition to a higher plateau, and independence of long-range electrostatic screening on chain conformation, can be encountered earlier with increasing flow strength, as a special feature of a polyelectrolyte in extensional-like flow. The translational self-diffusion coefficient increases when increasing either the flow strength or the electrostatic screening effect in uniform and simple shear flows. Scaling behavior of the static structure factor is quite well-correlated with respect to each flow field, where the Flory-Edwards exponent (${ u}$) decreases with higher values of flow strength and flow type parameters, but for lower screening effect. Present results on the mesoscopic scale devoted to the bulk space can readily serve as the basis for further scrutiny of the behavior of wormlike polyelectrolytes within various flow fields in confined spaces.