No, it is not right. Assuming the conical flask is the vessel in which the reaction takes place, it must be clean. If it is rinsed with distilled water, that’s fine. If it is rinsed with the solution under test that’s not fine - that will affect the number of molecules of reactant in the flask.
On the other hand … The volumetric flask or pipette that you use to load the conical flask must be rinsed with the solution under test to maintain its concentration. Likewise, the burette that you use to add your standard solution during the titration must be rinsed with the standard solution to avoid diluting it.
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