How have you set up your "list of keywords"?
One record for each keyword or do you have multiple keywords in the same field?
If in the same field, how are they entered in this field?
A script can build multiple find requests using this basic format:
Enter find Mode
Set field [Table::field ; //criteria goes here]
Set Field [Table::field ; //different criteriea here]
//repeat until all requests have been created
Set Error capture [on]
Perform Find 
The trick will be transporting the entire list of keywords from the first layout to the second so that the script can build these requests. How that works will depend on how the keywords are recorded in the "second table".
I just have each keyword in a new record in the "Keywords" table. I have each phrases in a individual record in the "Phrases" table.
My plan was to have the keywords table so that I could always add or remove a keyword from the search criteria. In excel, I could setup a query for this, but I don't see how to filter the "phrases" table so I am only showing phrases that contain a keyword from the "keywords" table.
Using what you have, this script would use the found set from the keywords table to filter your phrase list. (Note that you don't have to create and delete records in this table to change the keyword filter, you can include and omit existing records to make up different found sets of records instead.)
Go To Record/Request/Page [First]
Set Variable [$KeywordList ; Value: List ( $KeywordList ; KeywordTable::Keyword ) ]
Go To Record/Request/Page [next ; exit after last]
Go to layout [Phrases]
Enter Find Mode // clear the pause check box
Set Variable [$I ; Value: $I + 1]
Set Field [Phrases::Phrase ; GetValue ( $KeywordList ; $I ) ]
Exit Loop If [$I ≥ ValueCount ( $KeywordList )
Set Error Capture [on]
Sort [Restore ; No dialog ] //optional step here
It may also be possible to use a calculation field to break up your phrase into a list of keywords. Then a relationship between a text field that stores the list of keywords separated by returns could be used with Go To Related Records to pull up the desired phrases or they could be displayed in a portal.
Can I just hire you to build this for me?