If you are paid off by statement date it will have no impact to other banks (they won't see anything other than your highest balance, credit line, length of credit, any delinquencies, etc).

To chase, they may see your total spend favorably. In some instances excessive use on a bonus category and recycling a credit line is a negative (see AARP 5% account where people would turnover their credit line a lot in each month racking up thousands of rebates). I would imagine an amazon co-brand wouldn't be viewed as negatively since 1. 3% is only a good return (compared to 2% easily found), vs a great one; 2. The card is co-branded to a retailer who wants it to generate sales volume and may be sharing a portion of the program costs for the rebate.

You would have an easy case for a CLI if you wanted to use an inquiry on that. I'd do what another suggested and go for a new, different card and move the lines around later if the low limit is a problem.