This is what I could find going back through the book as far as Hurricane engagements:
Page 22 - Summary of fighting between March and June 1942. 64th Sentai lost 11 x Ki-43 and ten pilots. The author specifically notes here that 10 of the 11 were lost to AVG P-40s and 1 to a Blenheim. Allied losses were also 11 aircraft - 1 x P-40, 6 x Hurricanes, 2 x Hudsons, 1 x Blenheim, and 1 x B-17E.
This disparity in outcomes at this point can probably be attributable to the 'boom and zoom' tactics* which AVG was using right out the gate, but RAF took a while to adapt.
Page 26 - 9 December 1942, Hurricanes from 135 and 136 Sqns intercepted 24 Ki-43-Ib from 8th 50th and 64th Sentai escorting 21 x Ki-48s. The RAF fighters were bounced, and 2 x Hurricanes were shot down. No JAAF losses indicated.
15 December 1942, "action over Chittagong" 50th Sentai claimed 6 x Hurricanes and lost 1 x Ki-43 (no confirmation from Allied records shown here).
16 December 1942 50th Sentai was escorting 20 x Ki-51s and intercepted by Hurricanes from 607 and 615 Sqns. 3 x Hurricanes from 607 and 615 RAF shot down, plus 1 Hudson, for 1 x Ki-43-Ib (pilot captured).
20 December 1942 RAF raid with 12 Hurricanes escorting 14 Blenheims, intercepted by 3 x Ki-43s that scrambled from the base. Lt Nakazaki was hit by 20mm shells but claimed two Hurricanes, whiel Sgt. Anabuki claimed 1 Hurricane and a Blenheim (don't know if these are confirmed).
22 December 1942 50th Sentai claims 2 x Hurricanes for no loss (don't know if confirmed)
24 December 1942 Hurricane IIC attack Magwe. Six Ki-43 scramble to defend. Two Ki-43s were damaged (trailing white smoke) but shot down 2 x Hurricane IIC (Sgt E. Kostromin of 607 Sq and Flg Off C.D. Fergusson are named as shot down). Sgt Anabuki had forgotten to retract the undercarriage of his Ki-43. No Ki-43s were shot down, although one wrecked while landing (pilot survived).
14 January 1943 50th Sentai claimed 2 Hurricanes for no loss (don't know if confirmed)
18 January 1943 16 x Ki-43 from 50th Sentai escort 18 x Ki-21 to Chittagong. 2 Oscars return with engine trouble, the top cover of 2 x Ki-43s are bounced by 8 x Hurricanes from 136 and 3 x Hurricanes from 136 Sqn. Lt. Nakazaki's aircraft was badly damaged by 20mm canon shells. He crashed his plane into an allied ship and died. 50th Sentai claimed 3 but only got 1 Hurricane.
Loss Summary Dec 1942 - January 1943 50th Sentai claimed 40 victories. Actual Allied losses were 5 x Hurricane and 1 x P-40. 3 50th Sentai pilots were lost during this period.
12 February 1943 64th Sentai, now flying Ki-43-II are bounced by Mohawk IVs, CO Maj Masammi Yagi being killed.
13 February 1943 12 x Ki-43 escorting "light bombers" are bounced by 4 Hurricanes from No 261 Sqn. 2 x Ki-43-II were shot down, including 2nd Chutai leader Capt Jiro Seki. One Hurricane shot down (four claimed). On the way back to base they encounter 2 more Hurricanes from 79 Sqn, one Ki-43 engaged them and shot down one, pilot Sgt. R. North crash landing on a river beach.
20 February 1943 11 x Ki-43s escort 3 Ki-48. 3 x Hurricanes from No. 135 Sqn scrambled. 2 Hurricanes were destroyed, Plt Officer C Fox bailing out, Lt. G Booyson apparently killed. The third Hurricane was "badly shot up" but escaped. On 24 February 1943 the new 64th Sentai CO Major Akera shot down and killed by 51 FG P-40s.
28 February 1943 20 fighters from 50th and 64th Sentai both flying Ki-43-II attack a raid of 6 x Blenheims escorted by 7 Hurricanes from 136 Sqn. 2 x Hurricanes shot down (7 claimed), Sgt. P Kennedy and Sgt D Barnett bailing out. Sgt F Wilding belly landed back at Ramu airfield. No JAAF losses reported.
2 March 1943 50th Sentai claims 2 x Hurricanes, 64th Sentai later claims 2 more Hurricanes. I don't see any confirmation of these claims.
5 March 1943 64th Sentai engaged 136, 79 and 697 sqn escorting Blenheims. Claimed six, 1 Hurricane actually shot down for one Ki-43. In a second engagement with 135 Sqn 4 x Ki-43s were shot down for no RAF losses.
14 March 1943 64 Sentai fighter sweep of 15 Ki-43s encounters Blenheims escorted by 135 Sqn Hurricanes near Maungdaw. One Hurricane and one Blenheim shot down (author notes Kuroe fired 200 rounds at a Hurricane and it didn't go down, but his wingman finished it off. No JAAF losses reported here.
15 March 1943 14 x Ki-43 escorting 14 Ki-48 bombing Rathedaung. Had a 'meeting engagement' with a group of 12 Blenheims escorted by 136 and 607 Sqn. 4 x Hurricanes were shot down (Flg Officer F Pickard, Wt Off A Cruyenaeere (both 136 Sqn), and Flg W. Gibbs and Plot Off L. Main reported killed. One more Hurricane force-landed at Maungdaw. One Blenheim also destroyed. No JAAF losses indicated here.
17 March 1943 64th Sentai shot down a No. 79 Sqn Hurricane.
26 March 1943 50th Sentai claimes 3 x Hurricanes. (I did not see any Allied confirmation of this.)
27 March 1943 25 Ki-48s missed a rendezvous with 50th Sentai, and Hurricanes from 79 and 135 Sqn RAF shot down five of them for no loss.
28-30 March 1943 50th Sentai makes 38 claims but only 2 RAF planes are lost (1 x Hurricane and 1 x Mohawk IV)
31 March 1943 "Eight hand picked combat veterans" from 50th Sentai raid Allied airfield at Pataga. After strafing they climb to 19,000 ft and form "beehive" formation. Ten Hurricanes from 135 Sqn scrambled but are bounced. 50th Sentai claimed 8 shot down but actual losses were 3 x Hurricanes and one more "badly shot up".
2-4 April 1943 50th Sentai claims 8 victories (no confirmation here)
9 April 1943 16 x Ki-43-II from 64th Sentai bounced 9 x Hurricane II from 567 Sqn. 2 x Hurricanes shot down Sqn Leader J Bachmann killed.
Losses from 14 March - 11 April 1943. RAF claimed 20 victories and 20 probables. Actual JAAF losses were 9 aircraft - 5 x Ki-48, 3 x Ki-21, and 1 x Ki-36. No Ki-43s were lost in this period, though 23 were damaged. JAAF Ki-43 pilots claimed 416 aircraft. Actual RAF losses were 21 aircraft: 17 x Hurricanes, 1 x Mohawk IV, 1 x Beaufighter, 2 x Blenheims.
The author notes that these wildly exaggerated claims by the JAAF were more aircraft than the RAF actually had in the Theater at that time. The RAF overclaiming was much less, and is quite understandable considering that they damaged quite a few Ki-43s that managed to limp back to base. JAAF also claimed a large number of P-40s in this period but didn't actually get any.
There is more of this, but I think this is enough to show the pattern. The Hurricane usually came out with losses about 3-1 or 2-1 against them. They had a couple of good days but the vast majority of encounters went against them, and this included when the tactical situation was in their favor. I.e. even when the Hurricanes bounced the Ki-43s, they still usually lost. I'm not sure when the RAF adopted the hit and run tactics.
* it's worth noting that this "Boom and Zoom" was a little bit more subtle than the terse description usually goes, since numerous times in the book AVG and then 23rd FG pilots routinely got into long extended dog fights with Ki-43s and still came out on top, or at least survived.