Error Evaluating UI Expression Expression evaluation error at function a!gridField [line 27]: Could not find variable 'fv!row'

In your Columns setup, mouse over to show the expression editor, review what is defined in there.  This should be a list of a!gridColumn().  Feel free to post any further SAIL expressions in the thread here.  

there is no line 27 unfortunate.
is only the following 

a!linkField(
links: {
a!recordLink(
label: fv!row['recordType!{7c6cb0af-02e3-4e21-9db7-e5d7ebd92423}UMS AAPPs.fields.{aappNum}aappNum'],
recordType: 'recordType!{7c6cb0af-02e3-4e21-9db7-e5d7ebd92423}UMS AAPPs',
identifier: fv!row['recordType!{7c6cb0af-02e3-4e21-9db7-e5d7ebd92423}UMS AAPPs.fields.{aappNum}aappNum']
)
}
)

there is no line 27 unfortunate.
is only the following 

a!linkField(
links: {
a!recordLink(
label: fv!row['recordType!{7c6cb0af-02e3-4e21-9db7-e5d7ebd92423}UMS AAPPs.fields.{aappNum}aappNum'],
recordType: 'recordType!{7c6cb0af-02e3-4e21-9db7-e5d7ebd92423}UMS AAPPs',
identifier: fv!row['recordType!{7c6cb0af-02e3-4e21-9db7-e5d7ebd92423}UMS AAPPs.fields.{aappNum}aappNum']
)
}
)

This section expects a list of columns, you should update your code to

{
    a!gridColumn(
        label: "Link",
        value: a!linkField(
            links: {
                a!recordLink()
            }
        )
    )
}

Beat me to it

Utilizing the a!linkField() code provided here, this is how your expression should read.  Replace the above with:

{
  a!gridColumn(
    label: "Link",
    value: a!linkField(
      links: {
        a!recordLink(
          label: fv!row['recordType!{7c6cb0af-02e3-4e21-9db7-e5d7ebd92423}.fields.{aappNum}'],
          recordType: 'recordType!{7c6cb0af-02e3-4e21-9db7-e5d7ebd92423}',
          identifier: fv!row['recordType!{7c6cb0af-02e3-4e21-9db7-e5d7ebd92423}.fields.{aappNum}']
        )
      }
    )
  )
}