FPC Connector type for Echo Dot 2nd gen
It's a dual-row style FPC - essentially there are two rows of alternating contacts in the connector allowing for a tighter pitch on the ribbon cable.

Based on your measurements the pitch comes in at approximately 0.3mm, and I count 37 contacts.

Something along the lines of the Molex 504740 series such as 5047403700 which is a 37-pin dual row 0.3mm pitch connector.

To ensure compatibility, you'd need to also check that the depth difference between the contacts matches the FPC, along with the thickness of the kapton material.