How long does my insurance company have to respond when they receive a communication about a claim?

The answer is 14 calendar days!

627.70131 Insurer’s duty to acknowledge communications regarding claims; investigation.

(1)(a) Upon an insurer’s receiving a communication with respect to a claim, the insurer shall, within 14 calendar days, review and acknowledge receipt of such communication unless payment is made within that period of time or unless the failure to acknowledge is caused factors beyond the control of the insurer which reasonably prevent such acknowledgment. If the acknowledgment is not in writing, a notification indicating acknowledgment shall be made in the insurer’s claim file and dated. A communication made to or an agent of an insurer with respect to a claim shall constitute communication to or the insurer.