In some cases, we have to calibrate the Class A volumetric flask before analysis. In other cases, it is not necessary.
It is important to consider that some of these glass items come with batch certificate when the flask that has been calibrated is another flask. Other items come with an individual calibration certificate indicating the serial number of the flask. Another aspect is that there are manufacturers that produce volumetric glassware with prestigious brands and you know them, you can be confident that there is a high probability that the error of the instrument meets the maximum permissible error. There are other manufacturers that produce brands that you do not know and you have not the same reliability.
Thus, if your volumetric flask is new, it was manufactured with a prestigious brand and the contribution of the uncertainty of measurement of that volume will not significantly affect the result of your analysis, you can omit the calibration assuming that the error meets the maximum permissible error indicated by the manufacturer. In my opinion, you can use that criterion even if your certificate is not individual but is a lot certificate. An example like this can be found in the Eurachem/CITAC guide CG 4 "Quantifying Uncertainty in Analytical Measurement" (Third Edition, pages 38-39):
However, if you do not have these conditions it is recommended to calibrate the flask so that you know its error and the uncertainty of the error. In my opinion, you can use this criterion even if you have an individual certificate from a little known brand. This recommendation is based on the results obtained when calibrating volumetric instruments for about 15 years in the National Metrology Institute of Peru (INDECOPI, now called INACAL).
Abed Morales gave a rather circumstantial answer to your question. The essence of his answer is as follows: "…if your volumetric flask is new, it was manufactured with a prestigious brand and the contribution of the uncertainty of measurement of that volume will not significantly affect the result of your analysis, you can omit the calibration…". Still there are some things to add.
First, the flask may not be necessarily new; the capacity of the glassware can be thought practically unchanged with time unless, of course, the flask was used for preparation (and storage!) of corrosive liquids, such as strongly alkaline solutions, for which it is not recommended at all.
Second, a "prestigious brand" should simply mean a brand you can trust. Third, in routine chemical analysis, the uncertainty associated with the volumetric operation contributes quite insignificantly to the total uncertainty of the analytical result. To see this, just look at the volumetric tolerances (the maximum permissible errors) specified by a written standard to which the volumetric apparatus is made. (The component of volumetric uncertainty caused by the temperature variation is disregarded here.) As stated by ISO 1042, a 100 ml Class A volumetric flask has the tolerance equal to 0.10 ml, or 0.1 % in relative terms, and a 1000 ml Class A volumetric flask has the tolerance 0.40 ml, or 0.04 %. If we compare this percentage error with the relative error permitted in chemical analysis, which varies from a few percent to tens of percentages, the answer to the question about contribution of the volumetric uncertainty becomes evident. And so, it becomes evident the uselessness of the glassware calibration prior to analysis if other criteria mentioned above are met.
There may be situations where a much higher level of accuracy is required. Then, if necessary, specifically in case of Class B volumetric glassware, the uncertainty can be reduced by the use of individually calibrated apparatus rather than factory calibrated. Details concerning the use of volumetric apparatus and evaluation of its associated uncertainty can be found in:
Article Evaluation of measurement uncertainty in volumetric operatio...