How to smooth the separation between 2 hardboards on the floor?
The spacing you leave between the sheets of hardboard (or whatever other underlayment that you put down) will be determined from the manufacturer's instructions. Some materials need to have room for minor expansion over temperature and humidity ranges. If the proper gap is not left then the sheets of the material may buckle and create an uneven floor with bumps during some seasons. As such, if gaps are recommended then it would be advised to not try to fill them in with other materials. 

The material expansion characteristics of the underlayment need to be taken into careful account when considering what material types that you would lay and glue down over the underlayment. Make sure that the material (hardboard) that you are using is compatible with your vinyl material.

If large expansion gaps between your sheets of underlayment are say more than 1/8 inch (~3mm) then that may not be suitable for use under vinyl. Top load on the vinyl could cause the material to crack in places where it is pressed into the cracks. 

If you have a compatible underlayment material but have large gaps due to poor installation then you will have to either remove and replace the underlayment and bring gaps in line with 1/16" to 1/8". It may also be possible to trowel in a crack filler material between the sheets but that all depends upon the manufacturer's instructions regarding the expansion requirements for the underlayment material as stated previously.