What is the best method for confirming amyloidosis-
“The most definitive investigation for Amyloidosis is biopsy”.

For many years rectal biopsy was the first procedure of choice.
An important clinical advance was the recognition that the capillaries in the subcutaneous fat are often involved in patients with systemic amyloidosis and can often provide sufficient tissues for the diagnosis of amyloidosis. 
Thus, a biopsy of the organ with the most severe clinical involvement is often unnecessary.
For example in cardiac amyloidosis, the definitive diagnosis of the type of amyloid can be made using an endomyocardial biopsy specimen with Congo red and immunologic staining of the tissue sample.
Alternatively, when a noninvasive testing suggests cardiac amyloidosis - A specific diagnosis is often made by studying a subcutaneous fat aspiration instead of endomyocardial biopsy thereby avoiding an invasive procedure.
When the subcutaneous fat aspiration biopsy does not provide information to reach a firm diagnosis, biopsy samples can be collected from other organs.
In addition, an advantage to performing a biopsy of an involved organ (e.g., kidney heart) is that it definitively establishes a cause and effect relationship between the organ dysfunction and amyloid.
It is important to realize that not all biopsy sites offer the same sensitivity.

The best sites of biopsy are: -

Abdominal fat pad and (90% sensitivity)
Rectal mucosa (73% - 84% sensitivity)

Other sites that are often sampled but have poor sensitivity for the diagnosis of amyloid include: -

Salivary glands
Skin
Tongue
Gingiva
Stomach
Bone marrow
Colonoscopy
Sigmoidoscopy
Rectal biopsy
Tongue biopsy