There is no way to know for sure who the speaker of "Ex-Basketball Player" is. The narrator never explains who he or she is. All that the reader knows for sure is that the speaker of the poem was somebody that was able to watch Flick Webb play high school basketball.
I saw him rack up thirty-eight or forty
In one home game.
More than likely, the poem's speaker is a resident of the town where Flick plays. I think that because the speaker seems very familiar with the names of the streets and businesses that surround Flick Webb's current place of employment.
Pearl Avenue runs past the high-school lot,
Bends with the trolley tracks, and stops, cut off
Before it has a chance to go two blocks,
At Colonel McComsky Plaza.
Not only is the speaker familiar with the street names though, the speaker is familiar with Flick's current habits of bouncing inner tubes and going next door for a smoke at Mae's place. Those things all tell me that the speaker frequently sees Flick. That is most likely a town resident.
I also believe that the speaker is a native of the town, because he/she was able to see Flick play the home game where he racked up 40 points. The line makes it sound like that wasn't the only game the speaker was able to see. The speaker is just choosing to use that particular game to illustrate how good Flick was. It would be easiest for the poem's speaker to attend multiple home games, if he/she were a town resident.