ShellCheck already checks for bashism if the script is declared with #!/bin/sh, and finds most of the ones that checkbashisms does along with a few others. It's geared towards POSIX compliance though, and doesn't know which non-POSIX feature are available in e.g. busybox sh.
There is also some limited support for warning about features not available between non-POSIX shells, such as trying to use zsh =(temp files) in bash or bash ;;& case continuations in zsh, but this isn't as much of a focus as POSIX checks since it's not a common source of issues.
The Wooledge pitfall list was the original implementation checklist. About 38 out of the 46 are already covered in one form or another.
I haven't heard of Firehose before, but if you want to use it right now you can run shellcheck with -f gcc, to get gcc style error messages that Firehose can already parse.
Add support for the Firehose XML output format:
https://github.com/fedora-static-analysis/firehose
Checks for features that are specific to one shell (bashisms etc) when used with POSIX #!/bin/sh.
Checks for features that aren't implemented in the desired shell (for running on busybox sh for example).
Check for the various issues listed here:
http://mywiki.wooledge.org/BashPitfalls