Is it possible to pick next row's cell value on same column if condition not matched?
I assume you mean you want to find the "first" row with same Ticker_ID and same or bigger DateTime, first when ordered by DateTime ascending. One way to do this, assuming that the price table has a unique constraint on (Ticker_Ticker_ID, Price_DateTime):

UPDATE flaggedcomment AS fc 
    INNER JOIN price AS p
        ON  p.Ticker_Ticker_ID = fc.Ticker_Ticker_ID 
        AND p.Price_DateTime = 
            ( SELECT pi.Price_DateTime
              FROM price AS pi
              WHERE pi.Ticker_Ticker_ID = fc.Ticker_Ticker_ID 
                AND pi.Price_DateTime &gt;= fc.Comment_DateTime
              ORDER BY pi.Price_DateTime ASC
              LIMIT 1
            ) 
SET
    fc.Price_DateTime = p.Price_DateTime, 
    fc.Price_Open = p.Price_Open ;