Another goalless draw at The Hawthorns where again the Baggies have struggled to score at home for the third game running.
The result our sixth draw in a row sees us move to 5th in the table, next up is a trip to Hull City away on Sunday.
John Swift had a close range volley over the bar inside six minutes before Burnley had chances with Alex Palmer made saves to stop Flemming and former player Jeremy Sarmiento when he was so close.
Burnley had the ball in the net around the 59th minute mark as Jaidon Anthony headed the ball home, but unfortunately for the referee to rule it out with the Burnley forward having pushed Callum Styles.
The best opportunity fell to substitute Grady Diangana, however he could only guide his header off-target, ensuring that another draw was the case.
West Brom 0-0 Burnley
West Brom: Palmer; Furlong, Holgate, Heggem, Styles, Molumby, Mowatt (Racic 64), Fellows (Dobbin 64), Swift (Johnston 64), Grant (Cole 87), Maja (Diangana 81).
Burnley: Trafford, Esteve, Egan-Riley, Sarmiento (Laurent 76), Brownhill, Anthony, Roberts, Flemming, Pires, Cullen, Koleosho (Hannibal 90)
Another draw the 6th successive one and 8 games without a win and with all that we are still in the play-offs in 5th place. Next up is a game against Hull City on Sunday and we must start a good run before we could fall.