Is it possible to switch my early 98 f150 4x4 with a 78' bed from a styleside to a flareside?

 

You should only need to unbolt one bed, swap on the other...and probably swap fuel filler necks.

If they're both shortbeds, you're good, otherwise...

 

kjh98F150,
Yes, the beds will swap pretty easily, but there is a difference between the rear bumpers, too. If you get the flareside bed, make sure and get the matching rear bumper. Your styleside bumper won't fit.

Fordman3

 

Aren't the tailgates also different sizes?
You would need to swap those too.