Also move the implementation into a kernel so it can be more easily used. Follow-up to ARROW-13987.

Reporter: David Li / @lidavidm
Assignee: David Li / @lidavidm

Related issues:

• [C++] Support nested FieldRefs (is related to)

PRs and other links:

• GitHub Pull Request #11641

_{Note: This issue was originally created as ARROW-14615. Please see the migration documentation for further details.}