Brightline does not even connect with either airport as the stations are in Downtown FLL and Downtown Miami. As stated in AStarr's post, tri-rail has a shuttle that runs from FLL to the station at Griffin Road which you can board and take it to MIA where the station is at the Intermodal Center. You then will have to go upstairs and take the MIA Mover to the center of the Concourses near E/F on the third level, so you will have some walking to your check-in area once you arrive at MIA.

You can always grab the GO-shuttle curbside or make a reservation with SuperShuttle to take you to MIA.

MIA to FLL, you can grab Supershuttle curbside at MIA, or do the reverse by taking the MIA Mover to the Intermodal Center and then grab the Tri-Rail to the Griffin Road/FLL Airport station take the shuttle to the arrival level at FLL.