What are the disadvantages of fitting underwing flaps to a Mirage III/5 fighter jets to lower landing speeds?
Every airplane is a compromise of conflicting demands. While I am not intimately familiar with the Mirage family, I can easily see why flaps were never included.
In the early Fifties when work on deltas started at Dassault, the most important design parameter was top speed. High landing speeds were accepted, and given the design alternatives to a delta (think F-104), the landing speed could be considered low and another plus on the side of deltas.
When the first Mirage III were ordered, they had to serve in four different missions: As an advanced trainer (Mirage III B), an interceptor (Mirage III C), attack aircraft (Mirage III D and E) and for reconnaissance (Mirage III R). In order to allow for the widest variation in external loads, the lower wing should be free of flaps or other equipment which would restrict the attachment of tanks, armament or reconnaissance pods. Mounting any flaps at the straight trailing edge would require an opposite deflection of the elevons, negating any lift gain.
Flaps on naturally stable tailless aircraft are only helping if they are attached at a point ahead of the pitch trim flaps. This is possible with swept wings (see the Horten IX glider with its small flaps below) or with split flaps at mid-chord, like on the Gloster Javelin. With a straight trailing edge, no lift increase with a naturally stable configuration will be possible since the additional pitch moment of those flaps must be compensated at the same lengthwise location by the pitch control surfaces. What is gained with the flaps must be destroyed for pitch trim.

Horten IX V1 in tow, flaps lowered (picture source)
Since the Mirage line was never considered for use with aircraft carriers, its landing speed was accepted as part of the overall package. The Gloster Javelin was designed as a pure interceptor which put fewer demands on its lower wing. Also, the Javelin's tail helps to trim the aircraft in the landing configuration.
From the US translation of &quot;Aerodynamique de la Nouvelle Generation d'
Avions de Combat a Aile Delta&quot;, published in the AGARD Conference Proceedings No. 241:

Its [the Mirage III] aerodynamic formula, a delta wing swept back 60° at the leading edge, allowed Mach-2 flight with a single engine of 6 tonnes thrust, while its competitors were equipped with a 7-tonne J79.
The trade-off to this supersonic performance was a large increase
in the approach speed, 180 knots instead of 140 kt for the Mystere family. This constraint was accepted for the Mirage III, but later program specifications from the General Staff of the French Air Force required an approach speed below 150 kt.

So the Mirage III users had second thoughts, after all. The result of this lower approach speed requirement became the Mirage F-1.
Note that artificial stability allows to lower trailing edge flaps on a delta wing; the Mirage 2000 could be flown down to 100 kts airspeed.