Analyze each statement one by one

Biomolecules involved here are polysaccharides made from glucose units.

Option A: Amylose is a branched chain polymer of glucose

• Amylose is actually a linear polymer of glucose.
• It consists of b1-D-glucose units joined mainly by b1(1\to 4) glycosidic bonds.
• The branched component of starch is amylopectin, not amylose.

Therefore, Option A is incorrect.

Option B: Starch is a polymer of $\alpha$-D glucose

• Starch is made up of amylose and amylopectin.
• Both are polymers of $\alpha$-D-glucose.

Therefore, Option B is correct.

Option C: $\beta$-Glycosidic linkage makes cellulose polymer

• Cellulose is formed from $\beta$-D-glucose units.
• These units are connected through $\beta(1\to 4)$ glycosidic linkages.

Therefore, Option C is correct.

Option D: Glycogen is called as animal starch

• Glycogen is the storage polysaccharide in animals.
• Hence it is commonly called animal starch.

Therefore, Option D is correct.

Final conclusion

The only incorrect statement is: $\boxed{\text{A}}$

Comparison with stored correct answer

• Derived answer: A
• Stored correct answer: A

Both match.