Antibody test kits are NOT recommended at the moment by FDA and CDC to check if your vaccine is "working".
Antibody test kits have limited antibody specificity meaning you might test positive in some, and negative in others.
There are many reasons for this.
Most kits are not robust enough. It depends on how the kits were developed, because of the limitations (and cost), they might be tailored for certain parts of the virus or for only certain types of vaccines.
Most serology tests detect antibodies from the spike protein, while some detect the nucleocapsid protein.
Those kits targeting the nucleocapsid will not detect antibody response from vaccines that target the spike protein (e.g. Pfizer and AZ).