No. Bacteriostatic water is not flammable and is not regulated as a hazardous material for shipping. It is more than 99% water, and the 0.9% benzyl alcohol it contains has a flash point above 90 °C even in its pure form. Manufacturer safety data sheets generally classify the 0.9% solution as not hazardous under the GHS criteria, which is why it ships by ordinary ground and air services without hazard labeling. The SDS on file for the specific product governs.

Why the pure preservative and the product are classified differently

Benzyl alcohol as a neat chemical carries GHS hazard statements (it is classified as harmful if swallowed or inhaled and as an eye irritant) and is handled in the laboratory as any reagent is. Classification depends on concentration, and at 0.9% in water the solution falls below the thresholds at which those statements apply. The same distinction appears on the SDS for bacteriostatic water: the composition section names benzyl alcohol, while the classification section describes the mixture. See reading the safety data sheet and benzyl alcohol properties.

What still applies

• It is a chemical reagent in a glass container: it belongs in the laboratory’s chemical inventory with its SDS, and vials are handled with the usual care for glass.
• Storage is at 20–25 °C, protected from freezing. Heat is a product-quality issue, not a fire issue. See how to store bacteriostatic water.
• Disposal follows the laboratory’s rules for dilute aqueous chemical waste and for glass. See disposing of vials.
• Spills are wiped up with absorbent material; there is no vapor hazard from a few millilitres of a 0.9% solution, though the odor of benzyl alcohol is noticeable. See why does it have a smell?

Shipping

Because it is not a regulated hazardous material, bacteriostatic water ships in ordinary packaging; the constraints on transit are temperature and breakage, not hazard class. See how bacteriostatic water is shipped.

Related

Bacteriostatic water ingredients · What "research use only" means

All BAC Water Supply products are supplied for laboratory research use only and are not for human or veterinary use.