I have confirmed that the first query works as expected
<cfquery name="validation_info" dbtype="query">
    select      shipViaName,TOTALSHIPRATE
    from        s_c_c.qShipCalc
    WHERE       sku in (#preserveSingleQuotes(validate)#)
</cfquery>
<cfquery name="validation_info2" dbtype="query">
    select      TOTALSHIPRATE
    from        validation_info
    WHERE       shipViaName = "FedEx 3 Day"
</cfquery>
But on the second query, I get this error:
Encountered "shipViaName. Incorrect conditional expression, Incorrect conditional expression, Lexical error at line 0, column 0. Encountered: "\"" (34), after : ""
It says the error is happening on this line:
<cfquery name="validation_info2" dbtype="query">
I was also getting this error when I had the two queries combined into one.
Update from comments:
Dump of the validation_info query:
SHIPVIANAME TOTALSHIPRATE
1 | FedEx Ground | 11.9  ||
2 | FedEx 3 Day  | 22.99 || 
3 | FedEx 2 Day  | 26.99 || 
4 | FedEx 1 Day  | 44.55 || 
5 | FedEx Ground | 0     || 
6 | FedEx 3 Day  | 23.63 || 
7 | FedEx 2 Day  | 26.71 || 
8 | FedEx 1 Day  | 41.9  ||
 
                        
You need to use single quotes instead of double quotes for your string in your second SQL query.