GRAND CAYMAN TO CAYMAN BRAC
Cayman Brac is about 100 miles from Grand Cayman (half way to Cuba) so there is no ferry service. However, Cayman Airways fly from Grand Cayman to Cayman Brac about 6x per day.
There are 3 planes that fly:
Cost of Flights from Grand Cayman to Cayman Brac
An Economy ticket on any of these planes currently costs $87.38USD each way. Booking a return is no cheaper. Flights can be changed for $25USD
MIAMI TO CAYMAN BRAC
You can also fly direct from Miami to Cayman Brac on the Jet once a week, also with Cayman Airways. The weekly 1.5hr flight departs Miami at 12:50 on a Saturday and arrives at 1:20:
The outbound flight leaves Cayman Brac at 7am on Saturdays and takes longer (3hrs 40) as it stops in Grand Cayman but I don't believe you have to get off the plane:
Cost of Flights Miami to Cayman Brac
A return flight from Miami to Cayman Brac on these planes/dates is $421.32USD
GETTING TO GRAND CAYMAN
There are many airlines that fly to Grand Cayman. See here for information - Airline serving in Cayman Islands – CIAA (caymanairports.com)