How much should the front wheel flex
The amount a wheel will flex will vary greatly depending on front/rear, spoke count, rim material and rider weight.

The pedalling force that drives the bike passes through the rear wheel, so it is not uncommon for carbon rear wheels to flex significantly when a stronger/heavier rider is climbing.

For an aluminium rimmed front wheel with spokes that are correctly tensioned and a rider not exceeding the weight limit for the wheel then several mm of flex are not normal.