If you attack your opponent’s monster that has more ATK than your “Amazoness” monster, it will gain 1000 ATK automatically at the start of Damage Calculation. If your opponent then activates Honest, it will calculate the bonus based on the ATK of your monster after the 1000 ATK is added.
The effect "If an "Amazoness" monster attacks a monster with higher ATK, the attacking monster gains 1000 ATK during damage calculation only" does not make a Chain Link.
If there are multiple copies of "Amazoness Fighting Spirit", each one is applied during damage calculation one at a time, and if the opponent's monster targeted for the attack has "higher ATK [than] the attacking monster" that monster's ATK is increased. (For example, if it gains 1000 ATK due to the effect of the first "Amazoness Fighting Spirit" and then its ATK exceeds the opponent's monster, its ATK cannot be further increased by the effects of the second or later "Amazoness Fighting Spirit".)