You might find the Checkpoint gives you about the same position as the FX. You might need to shorten the stem a tad to get closer to the same reach from the saddle to the bars. But as far as bar height goes, the hoods and tops of the drop bar will be about the same height as the FX. Or at least close enough.
Out of the box from the LBS, you won't get the bars any higher on the FX or the Checkpoint than what the bike comes new with spacers under the stem. Probably 30 to 40mm worth. Either will require purchase of additional stuff such as stems angled steeply upward. Which, IMO, will just make it look dorky.
The Checkpoint being a road bike for drop bars will have a shorter frame reach going to the head tube than the FX a flat bar bike. That's due to the hand position on the flat bar having little to no additional reach to the hoods as does a drop bar bike. So putting a flat bar on the Checkpoint will mean you will have a shorter reach to the bars than you do on the FX with a flat bar. Maybe good maybe bad. The more upright you sit, the more you weight the saddle and the more sore your butt gets over the time of longer rides.
In addition you can't use the same STI's or whatever SRAM calls them if you change the Checkpoint to a flat bar. That will mean new shift and brake levers. And those usually are among the more expensive components in any group set.