The mixed anhydride, acetic formic anhydride (AFA), was first prepared by Béhal in 1899 who formed it by dissolving formic acid in acetic anhydride (AFM) in 1:1 mole ratio (Béhal, Compt. rend., 1899, 128, 1460)[1]. It was described as a liquid with an odor similar to that of acetic anhydride, boiling at about $\pu{29 ^\circ C}$ at a pressure of $\pu{18 torr}$. Similar to formic anhydride, which decomposes to formic acid and carbon monoxide ($\ce{CO}$) at room temperature within hours, AFA also decomposes slowly to acetic acid and $\ce{CO}$ by long standing at room temperature. For example, $\pu{50 mL}$ of AFM in a 100 mL volumetric flask with a rubber stopper had suddenly exploded after standing undisturbed for about 2 weeks [2]. Only $\ce{CO}$ (by flame test) and acetic acid in the flask were detected. The reaction was described as: $\ce{HC(=O)OC(=O)CH3 -> CO + CH3COOH}$.
The decomposition of AFA is accelerated by increasing temperature and types of catalyst used, and also depends upon the solvent used[1]: for instance, it is very fast in aprotic solvents such as toluene, carbon tetrachloride, and nitrobenzene, but slow in protic solvents such as ethanol, I-pentanol, and 2-methylpropanol (note that AFA undergoes formylation reaction of alcohols, instead of decomposition to $\ce{CO}$ and acetic acid; [3]). The catalyst for the decomposition could be either an acid (e.g., $\ce{H2SO4}$, $\ce{HNO3}$, $\ce{HF}$, $\ce{HCl}$, etc.) or tertiary amine bases (e.g., N,N-dimethylbenzeneamine, brucine, strychnine, nicotine, etc.), either of which produces $\ce{CO}$ and acetic acid. Note also that, a mixture of anhydrous $\ce{HF}$ and AFA at $\pu{0 ^\circ C}$ and atmospheric pressure produced formyl fluoride ($61\%$) with small amount of acetyl fluoride [4]. It’s noteworthy to mention that formyl fluoride is the only known stable halide of formic acid. The above reaction, however, depends on even relatively minor variations of conditions. For example, the reaction performed at room temperature instead of $\pu{0 ^\circ C}$ has yielded almost equimolar amounts of the formyl and acetyl fluorides [4]. Based on all of these evidences, it is safe to suggest that the most susceptible carbon center of AFA to a nucleophilic attack is the carbonyl carbon of its formyl group, but very sensitive to the reaction conditions.
Olah and others have done excellent work on AFA protonation [5]. According to $\ce{^1H}$ NMR evidence, they suggested rapid proton exchange between carbonyl oxygen atoms (observable at $\pu{-85 ^\circ C}$) of AFA and its eventual decomposition by excess super acids to protonated acetic and formic acids, acetyl cation, and formyl cation intermediate, which is not detected even at $\pu{-130 ^\circ C}$, but rapidly decomposed to $\ce{CO}$. Suggested mechanism and $\ce{^1H}$ NMR evidence are as follows:

Since, AFA gives formylated alcohols under similar condition in alcohols, the following mechanism can be suggested:

Yet, the major and minor product ratio is extremely depends on reaction conditions due to high sensitivity of AFA to its atmosphere.
Following example shows it can be used to selectively acylate (formylate) vide variety of heteroatoms if conditions are used accordingly [6].

References:
Strazzolini, P.; G. Giumanini, A.; Cauci, S. Acetic formic anhydride a review. Tetrahedron 1990, 46 (4), 1081-1118. DOI: 10.1016/S0040-4020(01)86676-X.
Schierz, E. R. The Catalytic Decomposition of Formic Acid in Acetic Anhudride: J. Am. Chem. Soc., 1923, 45(2), 455-468. DOI: 10.1021/ja01655a022.
Stevens, W.; van Es, A. Mixed Carboxylic Acid Anhydrides: II. Esterification of alcohols with the formic acid/acetic anhydride reaction mixture: Rec. Trav. Chim., 1964, 83(12), 1287-1293. DOI: 10.1002/recl.19640831212.
Olah, G. A.; Kuhn, S. J. Formylation with Formyl Fluoride: A New Aldehyde Synthesis and Formylation Method1. J. Am. Chem. Soc. 1960, 82 (9), 2380-2382. DOI: 10.1021/ja01494a065.
Olah, G. A.; Dunne, K.; Mo, Y. K.; Szilagyi, P. Stable carbocations. CXXVIII. Protonated acyclic carboxylic acid anhydrides and their cleavage to oxocarbenium ions. Question of the formyl cation in superacid media. J. Am. Chem. Soc. 1972, 94 (12), 4200-4205. DOI: 10.1021/ja00767a027.
Practical and Efficient Synthesis of N-Formylbenzotriazole: Org. Synth., 2013, 90, 358-366. DOI: 10.15227/orgsyn.090.0358.