Is this flicker lights dimming regularly then returning to normal for a period of time (motor starting inrush voltage drop?), or is this a constant flicker (loose conductor).
NOT NECESSARILY IN ORDER OF IMPORTANCE.
1. Two ground rods does not mean or do much for this issue.
2. Using a min max multimeter connect the meter at the service and watch for meter variances from steady state voltage.
3. Measure current at the same time. If you have flicker but no related current increases as there is VD then issue is upstream and may be a load by someone elese on the distribution system.
4. Measure voltage with the min max function at selected points throughout the house.
5. Check for ground current on GEC, EGCs, water pipe, at ground electrodes, with an eye on possible neutral issues.
6. Measure the current of L1, L2 and neutral simultaneously, the reading should be "0" amps.
7. Is this on L1 and L2 (more likely a neutral issue) or is it isolated to one of the "HOT" legs (this could be a loose energized conductor).
8. Check for thermal issue with all connections and circuit breakers utilizing a non-contact thermometer.
9. Perform *Fall of Potential (FOP) test across distribution components, the meter, main CB ECT.
10. NOTHING PERSONAL against the utility, BUT do not necessarily believe what they say. Many (not all) of these linemen know less that one would think. For that matter when trouble shooting I listen to everything anyone has to add to the topic, but do all investigations myself even if it was already looked at, especially if it has been looked at.
This does not cover all possible trouyble shooting ideas and others may have further ideas to add. PERCERVIENCE, the problem is there you just have to keep looking.
As little as 3.0 VAC drop Line to Neutral can result in noticeable light flicker
* from a another post
Fall of Potential test (FOP)
With any electrical procedures that involve making measurements with energized conductors care must be taken and proper PPE must be worn
Fall of potential is a measurement of voltage drop (VD), in a circuit that is the voltage lost to heating due to resistance in the circuit. To perform this test one measures voltage from the line side connections to the load side connections, the readings are typically in the millivolts range and require load.
For example with a 3-phase Circuit Breaker that is nuisance tripping, measure current (balance loads are beneficial but not necessary), then measure from the line bus to the load conductors (if bare conductor is exposed), for all three phases. If one phase has a higher that average millivolts reading, then try to isolate this issue. Measure from line bus to the Circuit Breaker bus stab, if all 3-phases have millivolts readings that are the same (or close to the same) measure from the bus stab to the load side conductor termination connector (through the Circuit Breaker), if all these readings are close, next take measurements from the load side termination connector to the load conductor. In this case you can determine if it is a line bus connection issue, bad Circuit Breaker or a load conductor termination issue. Any accessible portion of the device can be tested in this method.