Ignoring AFCI for this answer. AFCI is a more complex technology and I don't know how any AFCI-specific tester actually works. While in some areas, for new circuits, AFCI may be a requirement for kitchen receptacle circuits, the general requirement for many years is GFCI as that is a life-safety issue near water (such as kitchen sinks). In your case, you have AFCI and GFCI at the breaker. Most of this answer is the same for GFCI/receptacle as for GFCI/breaker or AFCI+GFCI/breaker (your situation).
The TEST button in a GFCI/receptacle or GFCI/breaker uses an internal mechanism which should work whether there is a ground connected or not. That is important as one of the key dangerous modes which a GFCI protects against is where some of the power goes through a person (typically due to water in the wrong place or damage to an appliance) to the physical, actual ground, such as through a barefoot person standing on a wet floor or touching a grounded metal-case appliance (stove, oven, refrigerator). 12A in on hot, 11.99A out on neutral, 0.01A (10 milliamps) through the person to physical ground is enough to trip a GFCI - and save a life.
However, the TEST button on a Magic 8-Ball Tester, a.k.a. three-light tester such as this one from Amazon:
works by sending that 10 milliamps to the ground pin of the receptacle. If that ground pin is not connected properly due to a break in the grounding system, including the possibility of no ground present in the receptacle box at all due to old wiring and no metal conduit then that TEST button will have no effect because it can't complete a circuit.
If indeed that is the case, there are a few options:
- Check the cables going into the panel. If they have black/white/ground then make sure the ground wire is connected properly. With a GFCI/breaker, neutral will be going to the breaker (and from the breaker to the neutral bar on a separate wire, unless it is a plug-on neutral breaker) but ground should be going to a ground bar. If they are black (or some other color) and white inside metal conduit then the metal conduit should provide the ground as long as you have metal conduit everywhere and metal boxes for the receptacles.
- Fix a problem within the receptacle box. It may be as simple as a plastic box (because with metal boxes normally grounding to good quality receptacles happens automagically) with a ground wire in it that was never connected to the ground screw of the GFCI/receptacle.
- Label the GFCI/receptacle, and any down-stream receptacles, to indicate that there is no ground. That is code-legal provided the circuit is an older circuit that pre-dates the requirement for a ground at every receptacle.
- Retrofit ground. It is now generally OK (depends on NEC version) to retrofit ground by running a ground wire from an unprotected receptacle to a protected receptacle or back to the panel. So if you have one circuit in the kitchen that has ground and one that doesn't, a jumper (green or bare wire, minimum 12 AWG) from a receptacle on one circuit to a receptacle on the other circuit should do the trick.