The following answer applies to a right triangle in a Euclidian plane.
The sum of the measures of the interior angles of ANY triangle is 180° A right angle measures 90° If a triangle had two right angles, then the sum of the measures of those two angles would be 90° + 90° = 180°. That would leave 0° for the third angle. So, in a word, the answer to your question is: No.
A triangle on the surface of a sphere, torus, or any sort of Reimann Surface has different properties.
