Okay, you're approaching this systematically, which is good. Here's a breakdown of potential causes and things to investigate, given the information you've provided

Possible Causes & Troubleshooting Steps:
Utility-Related Issues (Highly Suspect, Given Shared Transformer)



Transformer Overload

The most likely culprit, especially if the flickering happens consistently around the same time each day (3-4 PM). This is often a peak usage time.

Evidence

The time frame of 3-4 PM suggests increased demand on the transformer from other homes. Things like AC units kicking on, people getting home and using appliances, etc., could be straining the transformer.

Action



Inspect Transformer

(As you're planning) Look for signs of physical damage, overheating, or corrosion on the transformer. Do this visually and safely. Do not touch anything!



Talk to Neighbors

Ask if they're experiencing similar issues around the same time. This will strengthen the case that it's transformer-related.

Contact Utility Immediately

Report the problem to your electric utility. This is crucial. They are the only ones who can properly diagnose and fix transformer issues. Clearly explain the time correlation, the consistency, and that you suspect it's affecting multiple homes. Provide the dates and times you observed the flickering. The more specific you are, the faster they'll take action. Request they check the transformer's loading and voltage regulation.

Internal Wiring Issues (Less Likely, But Possible)



Loose Neutral Connection

A loose neutral is a classic cause of flickering and can affect multiple circuits.

Evidence

While less likely since you're observing it on multiple circuits and a voltage fluctuation would likely be observed, a corroded or loose neutral connection at the main panel could cause voltage imbalances across the legs.

Action



Check Main Panel Neutral

Important Safety Note: This is dangerous work. If you are not completely comfortable and qualified, DO NOT ATTEMPT THIS YOURSELF. Hire a licensed electrician. Carefully inspect the neutral connection at the main panel. Look for signs of corrosion, looseness, or burning. Tighten the connection if possible (again, ONLY if you are qualified and have disconnected power).

Check Neutral Connections at Each Affected Circuit

An electrician would also check neutral connections at the affected circuit breaker(s) and at the first receptacle/fixture in each circuit.

Loose Connections in Fixtures

A loose wire nut or connection inside a light fixture can cause flickering. However, it's unlikely to affect multiple circuits simultaneously.

Evidence

Single fixture or circuit affected.

Action



Inspect Fixtures

Turn off the power to the circuit and check the wire connections in any fixtures that flicker.

Overloaded Circuits

While you mentioned 15A circuits, it's good to double-check the load.

Evidence

Flipping occurs only when certain appliances are being used.

Action



Calculate Circuit Load

Add up the wattage of everything on each circuit that is on during the 3-4 PM window and compare it to the circuit's capacity (15A x 120V = 1800 watts).

LED Compatibility/Quality Issues (Less Likely, But Possible)



Dimmer Compatibility

Are any of the LEDs controlled by dimmers? If so, are the dimmers rated for LEDs?

Evidence

Flickering only occurs on dimmed lights or when using certain dimmers.

Action



Test Without Dimmer

If possible, bypass the dimmer switch temporarily to see if the flickering stops.

Use LED-Compatible Dimmers

Replace non-compatible dimmers with those specifically designed for LEDs.

Low-Quality LEDs

Cheap LEDs are more prone to flickering.

Evidence

Some LEDs flicker more than others.

Action



Replace Suspect Bulbs

Replace the most flickering bulbs with high-quality, reputable brand LEDs.

LED Driver Issues

LEDs use a driver to convert AC to DC. Failing or incompatible drivers can cause flickering.

Evidence

LED driver has failed or driver/bulb incompatibility.

Action



Replace Bulb

Replace suspect bulbs.

Appliance-Related Issues (Less Likely)



Large Appliances Cycling On/Off

A large appliance (like an AC unit, refrigerator compressor, or well pump) cycling on and off could cause a momentary voltage dip, but it should be brief and likely noticeable on your meter.

Evidence

Flickering consistently coincides with appliance cycles.

Action



Monitor Appliance Cycles

Pay attention to when large appliances cycle on and off and see if it correlates with the flickering.

Important Considerations



Safety First

When dealing with electrical wiring, always prioritize safety. Turn off the power at the breaker before working on any fixtures or wiring. If you're not comfortable, hire a qualified electrician.

Document Everything

Keep a detailed record of when the flickering occurs, which lights are affected, and any other relevant observations. This will be helpful for the utility or an electrician.

Multiple Issues

It's possible that you have a combination of issues. For example, a slightly overloaded transformer and some low-quality LEDs.

Steps in Order


Contact Utility Immediately

This should be your first step. Report the problem and emphasize the time correlation and potential transformer issue.2.

Gather Evidence for Utility

Document the dates and times the flickering occurred. Ask neighbors if they've experienced the same.3.

Inspect Transformer (Visually and Safely)

As you planned, but maintain a safe distance.4.

If Utility Doesn't Act Quickly

Consider hiring a qualified electrician to investigate the main panel neutral and potentially other wiring issues.5.

Test LED Dimmer Compatibility

If applicable, test dimmers.6.

Replace Suspect LED Bulbs:* If the flickering persists, start replacing low-quality LEDs with better ones.Good luck! It sounds like you're on the right track. The consistent timing points strongly toward a utility issue. Flag for review