The flag is often found on the graves of soldiers. In this case, the flag marks the service of English-born immigrant Chaplain Reverend W. B. Linell of Muncie, Indiana, who served during the Civil War in the 10th Illinois Regiment. Camp life was hard on his constitution and Linell, after a year of service, returned to his home in Indiana, tired, weak, and sick. Misfortune struck when his wife, who had a long-suffering illness, died. Linell recovered and served churches in Vevay and Muncie. The Universalist Register, in Linell’s biography, that he had set out for a convention in Terra Haute when “he was taken sick of typhoid fever, in Indianapolis, and was unable to reach his place of destination. He lay in a stupor, for several days, at the house of a friend, from, which he never awoke, till his eyes beheld the beatific world.”
Beech Grove Cemetery, Muncie, Indiana
Gravely Speaking 
I love the background information about the people as much as the information about the symbols used on their gravestones! Fascinating look into the past! Our current obituaries seem to always leave me with more questions than answers… the older ones answered questions before we even knew we had them….I like that!
One of the best representations I have ever seen of an American flag on a monument is in Pendleton, Indiana, which I believe you have visited. There are also great ones in Crown Hill in Indy.
I hope you will take a look at my latest post–I think this is the gravestone you were referring to in your comment about the monument with the flag in the Grove Lawn Cemetery in Pendleton. As you rightly point out it is one of the finest examples of a gravestone displaying the American flag.