Gibraltar hasn't been flooded with Brits. Native Gibraltar make up the majority of the population and are their own unique blend of Genoese, Andalusian, Maltese, Jewish and English. They are also a self governing British Overseas Territory - essentially independent but have a relationship of mutual support and shared foreign policy with the UK. Spain doesn't get to ride rough shod over their right to self-determination just because they share a land-border.
It is aggressive and extremely concerning that Spain and the EU are banding about threats regarding British and even American sovereignty. The focus should be on getting an arrangement that causes the least amount of upheaval for all current EU citizens (including UK citizens) and businesses.
Supporting the ceding of Gibraltar to Spain is no different from supporting the ceding of Alaska to Canada, Alsace to Germany, Kaliningrad to Poland or the Canary Islands and Cueta to Morocco. There are load of these national sovereignty anomalies that reflect complex human history and which are best not disturbed. Spain's response of trying to stick their oar into the Scottish independence debate is frankly laughable. How far should we take this small minded divisive talk? The next thing we know they will be supporting splitting the UK into Orkney and Shetland, Pictland, Scotland, Northumberland, Gwynedd, Dyfed, Cornwall... Then questions over Andalusia, Alsace, Brittany, Bavaria, Burgundy, Catalonia, Franconia, Lombardy, Sardinia and numerous other former nations having independent sovereignty might raise their heads and before you know it Europe will have thousands of independent movements and no cohesion. Clearly I jest a little, but simply to demonstrate it is completely daft to raise this sovereignty stuff as it opens a can of worms that will do more harm than good.