Two things that you can do to improve performance:
First (and most importantly) add a key or index to your tables. I don't know SQLite, but usually there's a command something like this:
CREATE INDEX DataIX1 ON Data(Symbol,EX)
You'll want one on the other table too:
CREATE INDEX SymbolExchangeIX1 ON Symbolexchange(Ticker,Exchange)
You may need to throw in ".." or '..' on the names...
The second thing is that although your first query is probably your best approach, you should only return the columns that you actually need/want:
SELECT Data.*
FROM Data
INNER JOIN Symbolexchange
ON Data.EX=Symbolexchange.EXCHANGE
AND Data.SYMBOL=Symbolexchange.TICKER