We'd definitely avoid using a structure like that where we had to repeat 'in'. In writing it looks really, really untidy and it is definitely best avoided. Happily enough it's easy enough to change: This form is to be filled in using black ink. 'This form is to fill in black ink' is not correct.

"This form is to be filled in in black ink" is 100% correct, but simply poor style. The two 'in's one after the other are right grammatically, but they just don't look good. You could reword it as Paul suggests, or as '"This form is to be completed in black ink".