If I open the hot and cold taps wide open on my tub, the water runs slow and it takes a long time to fill, But... If I open the tap on the bathroom sink, and just let water run down the drain, the flow rate to the tub increases, almost doubles in fact.

Usually it's the opposite. Flush a toilet and the flow of cold water to the shower or other toss Decreases.

In the bathroom the cold splits off to the sink, shower and tub. Have a 6 KW multipoint heater that feeds the sink, shower and tub with warm water.

Opening the sink tap only increases the tub tap flow rate if it's in the center, equal hot and cold. If I just turn on cold or just hot on the sink tap. The tub flow is the same as it is when all the other water taps in the house are shut off.

Any ideas why this happens?

Magic

Actually, it may be something to do with the valve in the water heater not responding correctly when the pressure/flow changes. Maybe it's blocked or has a faulty seal that allows it to do weird things.

My first thought was a flow sensor issue with the water heater. I didn't think the heaters did anything during operation to change the flow rate, I assumed it was restricted by the smaller tubing used to insure the water was in contact with the heating element long enough to heat up the water enough.

I don't think the plumbing is 100% sand-free so clogs might be a possibility. I've installed large filter to take care of the issue of sand coming up from the well but I didn't clean out all the fitting under the tub afterwards yet.

But if the water line to the tub is restricted enough for the heater to sense a low flow rate, how does it increase?

Probably stop valves that feed the faucets are rusted internally.

I hope not, the faucets, and the house are less than a year old. I suspect there is sand in the system because I noticed there is no cold water coming out of the tub faucet. That still doesn't explain why the hot water runs faster if I turn on another faucet in the same room.