What two phrases in Latin contain the same letters rearranged to translate as:
"Flee for I know the secrets of God" and "And I am free in the
country". I have seen these and was told that they were mottos of the
Merovingians; however, I have not found them and doubt the veracity of
the speakers claim to lineage.

Hello.

The two Latin phrases that you're thinking of are:

I tego Arcana Dei
Et in Arcadia Ego


source: 

'Better yet, an alternative interpretation is that the words "Et in
Arcadia Ego" are an anagram, and with a transposition and
rearrangement of the letters, becomes "I Tego Arcana Dei." This is a
Latin statement and can be translated as, "Begone!  I conceal the
Secrets of God!" '
http://www.halexandria.org/dward217.htm

'Et in Arcadia ego... is supposedly the official motto of the Priory
of Sion. Et in Arcadia ego is a Latin phrase, that most famously
appears as the title of a 17th century classical painting by French
painter Nicolas Poussin, which literally means, "And I in Arcadia."
However, the addition of three dashes is suggestive of the missing
word Sum in order for the phrase to be grammatically meaningful: "And
I am in Arcadia." Futhermore, it has been theorized by Richard Andrews
and Paul Schellenberger that the completed phrase Et in Arcadia ego
sum is an anagram for Arcam Dei Tango which means "I touch the tomb of
God."'
source:
World History - Priory of Sion
http://www.worldhistory.com/wiki/P/Priory-of-Sion.htm

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search strategy:
"i know the secrets of god"
"tego Arcana Dei" anagram

Right on the money and swift.

"Et in Arcadia ego sum" doesn't anagram to "Arcam Dei Tango," which is
shorter and has no s or u.

Apteryx

Well spotted, Apteryx.

Other web sites refer to:

"Et in Arcadia ego sum" &
"Arcam Dei Tango, Iesu"
://www.google.com/search?hl=en&ie=ISO-8859-1&q=%22+Arcam+Dei+Tango%22+sum&btnG=Google+Search

excellent!