Most hand sanitisers contain ethanol in concentrations > 60% (usually around 70-80%) which is classified as highly flammable (3.1B) under the hazardous substances legislation. It would be best to refer to the safety data sheet for specific advice on storage and use and for managing the risks. Even for small containers, there is a legal separation distance from ignition sources that must been maintained (not < 30cm for quantities less than 10 litres if I recall correctly), for flammable liquids of class 3.1A and B.
In the healthcare setting, there have been some rare examples of staff and patients causing ignition through static spark while using ethanol based hand sanitisers and before the ethanol has evapourated. See attached fire incident report from a hospital in Oregon, US. This is probably an extreme example as the patient had been playing with the hand sanitizer prior to the vapours igniting, but it makes for interesting reading non-the-less.
There is the following example of a healthcare worker suffering burns after ignition from static discharge but I have not as yet been able to find a credible incident or research report. https://www.improbable.com/2018/02/15/a-flash-fire-caused-by-a-hospital-hand-sanitizer/
Also the most recent newsletter from Responsible Care NZ also contains an example of an incident at a local transport company involving ignition of hand sanitizer that was ignited by static discharge before the ethanol had evapourated from the employees hands. The lesson here is to ensure that the hand sanitizer has been allowed to fully evapourate and that hands are clean and dry before commencing other tasks.
OHSU Feb 02 Report Final - Ethanol hand gel fire