[Casimiro Notevi]

No es Delphi, pero a ver si esto te sirve de referencia:

Private Sub SendInstallIntent
    Dim ApkName As String = kcTmpApk ''' "tmp.apk"
    Dim i As Intent
    If phone.SdkVersion >= 24 Then                                                    'Nougat 7.0
        i.Initialize("android.intent.action.INSTALL_PACKAGE", GetFileUri(ApkName))
        i.Flags = Bit.Or(i.Flags, 1) 'FLAG_GRANT_READ_URI_PERMISSION
    Else
        i.Initialize(i.ACTION_VIEW, "file://" & File.Combine(SharedFolder, ApkName))
        i.SetType("application/vnd.android.package-archive")
    End If
    StartActivity(i)
End Sub

Private Sub GetFileUri (FileName As String) As Object
    If UseFileProvider = False Then
        Dim uri As JavaObject
        Return uri.InitializeStatic("android.net.Uri").RunMethod("parse", Array("file://" & File.Combine(SharedFolder, FileName)))
    Else
        Dim f As JavaObject
        f.InitializeNewInstance("java.io.File", Array(SharedFolder, FileName))
        Dim fp As JavaObject
        Dim context As JavaObject
        context.InitializeContext
        fp.InitializeStatic("android.support.v4.content.FileProvider")
        Return fp.RunMethod("getUriForFile", Array(context, Application.PackageName & ".provider", f))
    End If
End Sub