can adopted children share some of the genetics as their adoptive parents?

Yes, they can if they were adopted by grandparents or other family members.

If they were to share any genetic similarities, it would be only by chance, unless there is a blood linkage.

Yes, adopting a relative is not at all uncommon. 

An aunt might adopt a niece or nephew, a parent might adopt a grandchild, etc.

this is a very stupid question.

Can they - sure - it might be possible - especially if someone adopts the child of a related person.  (aunts and uncles sometimes adopt their nieces or nephews if their sibling can't take care of the child - or grandparents adopt their grandchild if something has happened to their child.)

But, most adopted children would have very few genetic similarities to their adoptive parents.  A DNA test would show the differences easily.  

Most are chordates.

That answer used to be a YES orphans were adopted by the same genetic lines as their parents and raised in the same culture in modern times it become a Hodgepodge...

Talk about the LACK of being P.C...

N.Shadows 

Only if they were adopted by a blood relative of one of their biological parents. Your DNA is set at conception, it cannot be added to after the fact.

They might by chance, especially broad genetic traits such as skin tone, ear shape, blood type, etc.

Also, in a case where a relative of the birth parent adopted the baby, they would definately have some genetics in common. (For example, a teen pregnancy, and maybe an adult sibling adopts the baby.)