For a logical database design you don’t need to specify TINYINT or CHAR — that’s a physical consideration. Some DBMSes such as Postgres have a BOOLEAN data-type which would be preferred, but again, a physical design.
In your logical model you could assume a binary-valued datatype with Yes and No as the two values (or a ternary-valued type if NULL should also be allowed).
You have two questions actually; for the other, yes, I would keep the flag in the same relation.