Are the any Christian denominations that have doctrines in place that prohibit a national flag in the worship space? I am somewhat troubled by the presence of an American flag anywhere in a sanctuary / worship space. This sentiment is especially stark when said flag shares the same space / level as an altar.

I would like to see Christian doctrine / canon / by-laws or some other citation where this is prohibited, if at all.
For the Catholic Church, there are no universal norms (i.e., neither in Canon Law, nor in the various liturgical books) that prohibit national flags in the sanctuary (i.e., the space where the celebration of the Eucharist actually takes place). As a result, the norms regarding the use of flags, if any, are set by the diocesan bishop.

Generally, the U.S. Conference of Catholic Bishops has discouraged the use of national flags (and the U.S. is a country in which flags in the sanctuary have become relatively common), but there is no prohibition as such.

(The source for this is chiefly an article by Edward McNamara, L.C., from Zenit.org. To see the relevant section, scroll down to the paragraph beginning “Several readers asked about….”)