"Speedlight" is Nikon's brandname, and "Speedlite" is Canon's — but apparently Ricoh also used the name "Speedlite". That made me curious, and in a quick trademark search, it appears that no company has ever registered these terms, although an "American Speedlight Corporation" registered a letter-A-with-sunburst logo for their product ("Flash apparatus in which a capacitor is charged and thereafter discharged through a gas-filled tube to produce a flash of light").

That makes me suspect that the generic term actually predates any brand names, and indeed a Google Books search shows that it probably was generic before the current big brands' usage of it (even though these are old companies, their use of the word isn't ancient). The first reference I find is in National Geographic, from 1936 — but that turns out to be talking about Edgerton's work with actual high-speed strobe lighting, not the kind of portable flash you mean. After that, though, the term shows up quite consistantly in photo magazines starting around 1950, and clearly not in reference to any specific brand.

So, the history seems to make "speedlight" a pretty good generic choice, although (I think particularly because of pedantry about the Nikon/Canon loyalty divide) you might find yourself having to explain that you don't mean just Nikon. That suggests "speedlight-style" as a not completely unwieldy alternative less likely to provoke further need to explain — see for example "New Trigger Cable for Use with any Speedlight Style Flash". Or, you could use "speed light" with a space to distinguish from the brand.

Other options might include "hotshoe flash", which is fairly common, although when used with remote triggers (or via a cable) isn't necessarily completely accurate, as it might be a cold shoe. You could go with "shoe mount flash" and most people would know what you mean, but it sounds a little... awkward. B&H's "Speedlight Buyer’s Guide" also suggests "flashgun", and indeed that's also common (example: Digital Camera World; they use "flashgun" and "flash gun" inconsistently).

You'll also occasionally see the common style of flash called a "cobra flash", for the way it looks when bent to face forward. But, this is also sometimes used to refer to some pop-up flashes. And, not all hotshoe flashes follow this design, including budget non-tilt models, or — and here we are again pushing into the problem with "hotshoe flash", because another style is the "hammerhead flash", like the Metz mecablitz 45 CL, which is the same basic technology but meant to be attached to the camera via a bracket.

For completeness, Pentax just calls 'em "flash units" (even after the Ricoh acquisition), as does Metz; Sony and Olympus use "external flash units"; and Sigma seems to say "flashgun". But I still vote for "speedlight", "speed light", or "speedlight-style".