Czech “Border Check Request” form requirement on intra Schengen flight

No, you don’t need it. AIP says:

1.2.1.2.13 Detailed information about conditions for crossing external borders of the Czech Republic from the perspective of the Police of the CR – Alien Police service and Customs Administration of the CR has been published in aeronautical information circulars AIC A 5/16 and AIC C 9/13.

AIC A 5/16 says:

All aircraft commanders on an external flight other than performed by a commercial air transport operator (meaning the commanders of all General Aviation flights except the commanders of the Army of the Czech Republic, the Police of the Czech Republic and the NATO Armed Forces) for flights to all countries, except Austria, Poland, Hungary, Slovakia, Germany, Norway, Estonia, Lithuania, Latvia, Portugal, Spain, Malta, Sweden, Denmark, Finland, Iceland, France, Netherlands, Belgium, Luxembourg, Italy, Switzerland, Lichtenstein, Greece and Slovenia, i.e. the Schengen area Member States, will submit prior to departure from or arrival at an airport in the Czech Republic a Request for the Border Check (hereinafter “the request”).

Digging a bit deeper, down to the legislation: the Act No. 191/2016 Coll. on protection of state borders of the Czech Republic says:

§ 2 Basic concepts
(1) For the purposes of this Act:
a) a Member State is a state that applies the Schengen Borders Code in full,
b) an international flight is a flight from the territory of a Member State to the territory of a non-Member State, a flight from the territory of a non-Member State to the territory of a Member State, or a flight with a stopover in the territory of a non-Member State.

Thus, a flight from Sweden is not considered an international flight.