As @Cowgirl says, you may have to take the hive apart. However, having thought about it, I have another idea. The board is probably stuck with propolis. It is relatively flexible, and can be replaced if you damage it - core flute board is readily available from Amazon and stationery or art supply shops. So, why not try inserting your flow key above it? I would actually prefer a thin metal rule (often incorrectly called a ruler), but you would need one more than 20 inches long, like this one:
https://www.amazon.com/Starrett-ASE-36-Anodized-Aluminum-Straight/dp/B002C7YX3O/ref=pd_sbs_469_2?ie=UTF8&psc=1&refRID=GWAG5TPSEJ4F2MQTXBSY
You will need to be careful not to distort the wire mesh of the SBB, but that shouldn’t be too hard. Push it in as far as it will go, and move the key (or rule) from side to side. That should unstick it from the mesh. It may be stuck at the edges still, but the flexing of the slider might even loosen it there too. Perhaps worth a try before you take the hive apart? 
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