“Love kindled by virtue always kindles another, provided that its flame appear outwardly.”

No findable citation to Socrates. First appears in this form in the 1990s, such as in the Douglas Bradley article "Lighting a Flame in the Kickapoo Valley", Wisconsin Ideas, UW System, 1994. It appears to be a variant on a statement from Plutarch in On Listening to Lectures: "The correct analogy for the mind is not a vessel that needs filling, but wood that needs igniting — no more — and then it motivates one towards originality and instills the desire for truth." Alternate translation, from the Loeb Classical Library edition, 1927 http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/De_auditu*.html: "For the mind does not require filling like a bottle, but rather, like wood, it only requires kindling to create in it an impulse to think independently and an ardent desire for the truth." Often quoted as, "The mind is not a vessel to be filled but a fire to be kindled." Variants of the quote that are correctly attributed to Plutarch but which substitute "education" for "the mind" date back at least as far as the 1960s, as seen in the 1968 book Vision and Image by James Johnson Sweeney, p. 119 http://books.google.com/books?id=d58FAAAAMAAJ&q=plutarch#search_anchor.
Variants with "education" are also sometimes misattributed to William Butler Yeats, as in the 1993 book The Harper Book of Quotations (third edition), p. 138 http://books.google.com/books?id=THl7kUfSqCUC&lpg=PP1&pg=PA138#v=onepage&q&f=false. In the previously-mentioned Vision and Image, the misquote of Plutarch involving "education" (which has exactly the same wording as the quote attributed to Yeats in The Harper Book of Quotations) is immediately preceded by a different quote from Yeats ("Culture does not consist in acquiring opinions but in getting rid of them"), so it's possible this is the source of the confusion—see the snippets here http://books.google.com/books?id=d58FAAAAMAAJ&q=yeats+culture#search_anchor and here http://books.google.com/books?id=d58FAAAAMAAJ&q=%22getting+rid+of+them%22#search_anchor.
The misattribution may also be related to a statement about Plato's views made by Benjamin Jowett in the introduction to his translation of Plato's Republic (in which all the main ideas were attributed to Socrates, as in all of Plato's works), on p. cci http://books.google.com/books?id=Cg_QX4yoOSQC&pg=PR201#v=onepage&q&f=false of the third edition (1888): "Education is represented by him, not as the filling of a vessel, but as the turning the eye of the soul towards the light." Jowett seems to be loosely paraphrasing a statement Plato attributes to Socrates in a dialogue with Glaucon, in sections 518b http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0168%3Abook%3D7%3Asection%3D518b– 518c http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0168%3Abook%3D7%3Asection%3D518c of book 7 of The Republic, where Socrates says: "education is not in reality what some people proclaim it to be in their professions. What they aver is that they can put true knowledge into a soul that does not possess it, as if they were inserting vision into blind eyes … But our present argument indicates that the true analogy for this indwelling power in the soul and the instrument whereby each of us apprehends is that of an eye that could not be converted to the light from the darkness except by turning the whole body."
Further discussion of the history of this quote can be found in this entry http://quoteinvestigator.com/2013/03/28/mind-fire/ from the "Quote Investigator" website.
Misattributed

Lectures on the English Poets http://www.gutenberg.org/files/16209/16209.txt (1818), Lecture VIII, "On the Living Poets"

Todos los soles se esfuerzan en encender tu llama y un microbio la extingue.
Voces (1943)

Life: Relish It! p. 127.
Love: Be it! (2001)

Prologue (p. 1)
The Enemy Stars (1959)

Source: Social Problems (1883), Ch. 21 : Conclusion
Context: Many there are, too depressed, too embruted with hard toil and the struggle for animal existence, to think for themselves. Therefore the obligation devolves with all the more force on those who can. If thinking men are few, they are for that reason all the more powerful. Let no man imagine that he has no influence. Whoever he may be, and wherever he may be placed, the man who thinks becomes a light and a power. That for every idle word men may speak they shall give an account at the day of judgment, seems a hard saying. But what more clear than that the theory of the persistence of force, which teaches us that every movement continues to act and react, must apply as well to the universe of mind as to that of matter? Whoever becomes imbued with a noble idea kindles a flame from which other torches are lit, and influences those with whom he comes in contact, be they few or many. How far that influence, thus perpetuated, may extend, it is not given to him here to see. But it may be that the Lord of the Vineyard will know.

"Lord Of All Being" (1848).

Source: Essay on Translated Verse (1684), Line 173.