Bag limit is for one day. You need to check the possession limit. As stated above this does not apply to flounder.
Flounder special regulation: Daily bag is 5 fish except for the period Nov. 1-30 when the daily bag is 2 fish and flounder may be taken only by pole and line.
Possession limit is equal to the daily bag.
Possession Limit: The maximum number of fish a person may possess before returning to their permanent residence. Possession limit is twice the daily bag on game and nongame fish, except as provided in this guide, and does not apply to fish in the possession of or stored by a person at their permanent residence.
Reference:
http://www.tpwd.state.tx.us/regulati...initions.phtml