The verse doesn't refer to runaway American slaves fleeing from their former masters. It means slaves who were fighting with the British against the United States during the War of 1812.
These would be slaves who were "impressed" (forced or employed into military services) by the British and hence enemies of the United States (for any cause), but not simply "runaway slaves." Alternatively, the verse may even be referring to British mercenaries themselves.
The verse in question, in context:
And where are the foes that so vauntingly swore
That the havoc of war & the battle's confusion
A home and a Country should leave us no more?
Their blood has wash'd out their foul footstep's pollution.
No refuge could save—the hireling & slave
From the terror of flight, or the gloom of the grave,
And the star-spangled banner in triumph doth wave
O'er the land of the free & the home of the brave.
The Star Spangled Banner lyrics "the hireling " refers to the British use of Mercenaries (German Hessians) in the American War of Independence
The Star Spangled Banner lyrics "...and slave" is a direct reference to the British practice of Impressment (kidnapping American seamen and forcing them into service on British man-of war ships). This was a Important cause of the War of 1812
Francis Scott Key then describes the Star Spangled Banner as a symbol of triumph over all adversity
Snopes also debunked your view:
In fairness, it has also been argued that Key may have intended the phrase as a reference to the British Navy's practice of impressment (kidnapping sailors and forcing them to fight in defense of the crown), or as a semi-metaphorical slap at the British invading force as a whole (which included a large number of mercenaries), though the latter line of thinking suggests an even stronger alternative theory — namely, that the word "hirelings" refers literally to mercenaries and "slaves" refers literally to slaves. It doesn't appear that Francis Scott Key ever specified what he did mean by the phrase, nor does its context point to a single, definitive interpretation.
http://www.snopes.com/2016/08/29/star-spangled-banner-and-slavery/
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